42,895 research outputs found
Sequencing Chess
We analyze the structure of the state space of chess by means of transition
path sampling Monte Carlo simulation. Based on the typical number of moves
required to transpose a given configuration of chess pieces into another, we
conclude that the state space consists of several pockets between which
transitions are rare. Skilled players explore an even smaller subset of
positions that populate some of these pockets only very sparsely. These results
suggest that the usual measures to estimate both, the size of the state space
and the size of the tree of legal moves, are not unique indicators of the
complexity of the game, but that topological considerations are equally
important
Rotation-supported Neutrino-driven Supernova Explosions in Three Dimensions and the Critical Luminosity Condition
We present the first self-consistent, three-dimensional (3D) core-collapse
supernova simulations performed with the Prometheus-Vertex code for a rotating
progenitor star. Besides using the angular momentum of the 15 solar-mass model
as obtained in the stellar evolution calculation with an angular frequency of
about 0.001 rad/s (spin period of more than 6000 s) at the Si/Si-O interface,
we also computed 2D and 3D cases with no rotation and with a ~300 times shorter
rotation period and different angular resolutions. In 2D, only the nonrotating
and slowly rotating models explode, while rapid rotation prevents an explosion
within 500 ms after bounce because of lower radiated neutrino luminosities and
mean energies and thus reduced neutrino heating. In contrast, only the fast
rotating model develops an explosion in 3D when the Si/Si-O interface collapses
through the shock. The explosion becomes possible by the support of a powerful
SASI spiral mode, which compensates for the reduced neutrino heating and pushes
strong shock expansion in the equatorial plane. Fast rotation in 3D leads to a
"two-dimensionalization" of the turbulent energy spectrum (yielding roughly a
-3 instead of a -5/3 power-law slope at intermediate wavelengths) with enhanced
kinetic energy on the largest spatial scales. We also introduce a
generalization of the "universal critical luminosity condition" of Summa et al.
(2016) to account for the effects of rotation, and demonstrate its viability
for a set of more than 40 core-collapse simulations including 9 and 20
solar-mass progenitors as well as black-hole forming cases of 40 and 75
solar-mass stars to be discussed in forthcoming papers.Comment: 24 pages, 19 figures; refereed version with additional section on
resolution dependence; accepted by Ap
Critical Behavior of the Antiferromagnetic Heisenberg Model on a Stacked Triangular Lattice
We estimate, using a large-scale Monte Carlo simulation, the critical
exponents of the antiferromagnetic Heisenberg model on a stacked triangular
lattice. We obtain the following estimates: ,
. These results contradict a perturbative
Renormalization Group calculation that points to Wilson-Fisher O(4) behaviour.
While these results may be coherent with results from
Landau-Ginzburg analysis, they show the existence of an unexpectedly rich
structure of the Renormalization Group flow as a function of the dimensionality
and the number of components of the order parameter.Comment: Latex file, 10 pages, 1 PostScript figure. Was posted with a wrong
Title !
On the Ricci tensor in type II B string theory
Let be a metric connection with totally skew-symmetric torsion \T
on a Riemannian manifold. Given a spinor field and a dilaton function
, the basic equations in type II B string theory are \bdm \nabla \Psi =
0, \quad \delta(\T) = a \cdot \big(d \Phi \haken \T \big), \quad \T \cdot \Psi
= b \cdot d \Phi \cdot \Psi + \mu \cdot \Psi . \edm We derive some relations
between the length ||\T||^2 of the torsion form, the scalar curvature of
, the dilaton function and the parameters . The main
results deal with the divergence of the Ricci tensor \Ric^{\nabla} of the
connection. In particular, if the supersymmetry is non-trivial and if
the conditions \bdm (d \Phi \haken \T) \haken \T = 0, \quad \delta^{\nabla}(d
\T) \cdot \Psi = 0 \edm hold, then the energy-momentum tensor is
divergence-free. We show that the latter condition is satisfied in many
examples constructed out of special geometries. A special case is . Then
the divergence of the energy-momentum tensor vanishes if and only if one
condition \delta^{\nabla}(d \T) \cdot \Psi = 0 holds. Strong models (d \T =
0) have this property, but there are examples with \delta^{\nabla}(d \T) \neq
0 and \delta^{\nabla}(d \T) \cdot \Psi = 0.Comment: 9 pages, Latex2
Supernova Simulations from a 3D Progenitor Model -- Impact of Perturbations and Evolution of Explosion Properties
We study the impact of large-scale perturbations from convective shell
burning on the core-collapse supernova explosion mechanism using
three-dimensional (3D) multi-group neutrino hydrodynamics simulations of an 18
solar mass progenitor. Seed asphericities in the O shell, obtained from a
recent 3D model of O shell burning, help trigger a neutrino-driven explosion
330ms after bounce whereas the shock is not revived in a model based on a
spherically symmetric progenitor for at least another 300ms. We tentatively
infer a reduction of the critical luminosity for shock revival by ~20% due to
pre-collapse perturbations. This indicates that convective seed perturbations
play an important role in the explosion mechanism in some progenitors. We
follow the evolution of the 18 solar mass model into the explosion phase for
more than 2s and find that the cycle of accretion and mass ejection is still
ongoing at this stage. With a preliminary value of 0.77 Bethe for the
diagnostic explosion energy, a baryonic neutron star mass of 1.85 solar masses,
a neutron star kick of ~600km/s and a neutron star spin period of ~20ms at the
end of the simulation, the explosion and remnant properties are slightly
atypical, but still lie comfortably within the observed distribution. Although
more refined simulations and a larger survey of progenitors are still called
for, this suggests that a solution to the problem of shock revival and
explosion energies in the ballpark of observations are within reach for
neutrino-driven explosions in 3D.Comment: 23 pages, 22 figures, accepted for publication in MNRA
Four-body structure of Li and spin-dependent interaction
Two spin-doublet states of %- and - in
Li are studied on the basis of the
four-body model. We employ the two-body interactions which reproduce the
observed properties of any subsystems composed of ,
and , and . Furthermore, the
interaction is adjusted so as to reproduce the - splitting of in
H. The calculated energy splittings of - and
- states in Li are 0.69 MeV and 0.46 MeV, which are
in good agreement with the resent observed data. The spin-dependent components
of the interaction are discussed.Comment: 6 pages, 2 figures, published to be in Phys. Rev.
The Dynamical Cluster Approximation (DCA) versus the Cellular Dynamical Mean Field Theory (CDMFT) in strongly correlated electrons systems
We are commenting on the article Phys. Rev. {\bf B 65}, 155112 (2002) by G.
Biroli and G. Kotliar in which they make a comparison between two cluster
techniques, the {\it Cellular Dynamical Mean Field Theory} (CDMFT) and the {\it
Dynamical Cluster Approximation} (DCA). Based upon an incorrect implementation
of the DCA technique in their work, they conclude that the CDMFT is a faster
converging technique than the DCA. We present the correct DCA prescription for
the particular model Hamiltonian studied in their article and conclude that the
DCA, once implemented correctly, is a faster converging technique for the
quantities averaged over the cluster. We also refer to their latest response to
our comment where they argue that instead of averaging over the cluster, local
observables should be calculated in the bulk of the cluster which indeed makes
them converge much faster in the CDMFT than in the DCA. We however show that in
their original work, the authors themselves use the cluster averaged quantities
to draw their conclusions in favor of using the CDMFT over the DCA.Comment: Comment on Phys. Rev. B 65, 155112 (2002). 3 pages, 2 figure
Hyperon mixing and universal many-body repulsion in neutron stars
A multi-pomeron exchange potential (MPP) is proposed as a model for the
universal many-body repulsion in baryonic systems on the basis of the Extended
Soft Core (ESC) bryon-baryon interaction. The strength of MPP is determined by
analyzing the nucleus-nucleus scattering with the G-matrix folding model. The
interaction in channels is shown to reproduce well the experimental
binding energies. The equation of state (EoS) in neutron matter with
hyperon mixing is obtained including the MPP contribution, and mass-radius
relations of neutron stars are derived. It is shown that the maximum mass can
be larger than the observed one even in the case of including
hyperon mixing on the basis of model-parameters determined by terrestrial
experiments
Neutron-star radii based on realistic nuclear interactions
The existence of neutron stars with requires the strong stiffness
of the equation of state (EoS) of neutron-star matter. We introduce a
multi-pomeron exchange potential (MPP) working universally among 3- and
4-baryons to stiffen the EoS. Its strength is restricted by analyzing the
nucleus-nucleus scattering with the G-matrix folding model. The EoSs are
derived using the Brueckner-Hartree-Fock (BHF) and the cluster variational
method (CVM) with the nuclear interactions ESC and AV18. The mass-radius
relations are derived by solving the Tolmann-Oppenheimer-Volkoff (TOV)
equation, where the maximum masses over are obtained on the basis of
the terrestrial data. Neutron-star radii at a typical mass are
predicted to be km. The uncertainty of calculated radii is
mainly from the ratio of 3- and 4-pomeron coupling constants, which cannot be
fixed by any terrestrial experiment. Though values of are not
influenced by hyperon-mixing effects, finely-observed values for them indicate
degrees of EoS softening by hyperon mixing in the region of
. If is less than about 12.4 km, the
softening of EoS by hyperon mixing has to be weak. Useful information can be
expected by the space mission NICER offering precise measurements for
neutron-star radii within .Comment: 8 pages, 7 figure
Sub-Hz line width diode lasers by stabilization to vibrationally and thermally compensated ULE Fabry-Perot cavities
We achieved a 0.5 Hz optical beat note line width with ~ 0.1 Hz/s frequency
drift at 972 nm between two external cavity diode lasers independently
stabilized to two vertically mounted Fabry-Perot (FP) reference cavities.
Vertical FP reference cavities are suspended in mid-plane such that the
influence of vertical vibrations to the mirror separation is significantly
suppressed. This makes the setup virtually immune for vertical vibrations that
are more difficult to isolate than the horizontal vibrations. To compensate for
thermal drifts the FP spacers are made from Ultra-Low-Expansion (ULE) glass
which possesses a zero linear expansion coefficient. A new design using Peltier
elements in vacuum allows operation at an optimal temperature where the
quadratic temperature expansion of the ULE could be eliminated as well. The
measured linear drift of such ULE FP cavity of 63 mHz/s was due to material
aging and the residual frequency fluctuations were less than 40 Hz during 16
hours of measurement. Some part of the temperature-caused drift is attributed
to the thermal expansion of the mirror coatings. High-frequency thermal
fluctuations that cause vibrations of the mirror surfaces limit the stability
of a well designed reference cavity. By comparing two similar laser systems we
obtain an Allan instability of 2*10-15 between 0.1 and 10 s averaging time,
which is close to the theoretical thermal noise limit.Comment: submitted to Applied Physics
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