725 research outputs found
Effect of the Canting of Local Anisotropy Axes on Ground-State Properties of a Ferrimagnetic Chain with Regularly Alternating Ising and Heisenberg Spins
The effect of the canting of local anisotropy axes on the ground-state phase
diagram and magnetization of a ferrimagnetic chain with regularly alternating
Ising and Heisenberg spins is exactly examined in an arbitrarily oriented
magnetic field. It is shown that individual contributions of Ising and
Heisenberg spins to the total magnetization basically depend on the spatial
orientation of the magnetic field and the canting angle between two different
local anisotropy axes of the Ising spins.Comment: 3 pages, 3 figure
On the rate of black hole binary mergers in galactic nuclei due to dynamical hardening
We assess the contribution of dynamical hardening by direct three-body
scattering interactions to the rate of stellar-mass black hole binary (BHB)
mergers in galactic nuclei. We derive an analytic model for the single-binary
encounter rate in a nucleus with spherical and disk components hosting a
super-massive black hole (SMBH). We determine the total number of encounters
needed to harden a BHB to the point that inspiral due to
gravitational wave emission occurs before the next three-body scattering event.
This is done independently for both the spherical and disk components. Using a
Monte Carlo approach, we refine our calculations for to include
gravitational wave emission between scattering events. For astrophysically
plausible models we find that typically 10.
We find two separate regimes for the efficient dynamical hardening of BHBs:
(1) spherical star clusters with high central densities, low velocity
dispersions and no significant Keplerian component; and (2) migration traps in
disks around SMBHs lacking any significant spherical stellar component in the
vicinity of the migration trap, which is expected due to effective orbital
inclination reduction of any spherical population by the disk. We also find a
weak correlation between the ratio of the second-order velocity moment to
velocity dispersion in galactic nuclei and the rate of BHB mergers, where this
ratio is a proxy for the ratio between the rotation- and dispersion-supported
components. Because disks enforce planar interactions that are efficient in
hardening BHBs, particularly in migration traps, they have high merger rates
that can contribute significantly to the rate of BHB mergers detected by the
advanced Laser Interferometer Gravitational-Wave Observatory.Comment: 13 pages, 9 figures, accepted for publication in MNRA
Additive and heterozygous (dis)advantage GWAS models reveal candidate genes involved in the genotypic variation of maize hybrids to Azospirillum brasilense
Optimization Heuristics for Determining Internal Rating Grading Scales
Basel II imposes regulatory capital on banks related to the default risk of their credit portfolio. Banks using an internal rating approach compute the regulatory capital from pooled probabilities of default. These pooled probabilities can be calculated by clustering credit borrowers into different buckets and computing the mean PD for each bucket. The clustering problem can become very complex when Basel II regulations and real-world constraints are taken into account. Search heuristics have already proven remarkable performance in tackling this problem. A Threshold Accepting algorithm is proposed, which exploits the inherent discrete nature of the clustering problem. This algorithm is found to outperform alternative methodologies already proposed in the literature, such as standard k-means and Differential Evolution. Besides considering several clustering objectives for a given number of buckets, we extend the analysis further by introducing new methods to determine the optimal number of buckets in which to cluster banks’ clients
A nonextensive approach to the dynamics of financial observables
We present results about financial market observables, specifically returns
and traded volumes. They are obtained within the current nonextensive
statistical mechanical framework based on the entropy
(). More precisely, we
present stochastic dynamical mechanisms which mimic probability density
functions empirically observed. These mechanisms provide possible
interpretations for the emergence of the entropic indices in the time
evolution of the corresponding observables. In addition to this, through
multi-fractal analysis of return time series, we verify that the dual relation
is numerically satisfied, and being
associated to the probability density function and to the sensitivity to
initial conditions respectively. This type of simple relation, whose
understanding remains ellusive, has been empirically verified in various other
systems.Comment: Invited paper to appear in special issue of Eur. Phys. J. B dedicated
to econophysics, edited by T. Di Matteo and T. Aste. 7 page
An extended-phase-space dynamics for the generalized nonextensive thermostatistics
We apply a variant of the Nose-Hoover thermostat to derive the Hamiltonian of
a nonextensive system that is compatible with the canonical ensemble of the
generalized thermostatistics of Tsallis. This microdynamical approach provides
a deterministic connection between the generalized nonextensive entropy and
power law behavior. For the case of a simple one-dimensional harmonic
oscillator, we confirm by numerical simulation of the dynamics that the
distribution of energy H follows precisely the canonical q-statistics for
different values of the parameter q. The approach is further tested for
classical many-particle systems by means of molecular dynamics simulations. The
results indicate that the intrinsic nonlinear features of the nonextensive
formalism are capable to generate energy fluctuations that obey anomalous
probability laws. For q<1 a broad distribution of energy is observed, while for
q>1 the resulting distribution is confined to a compact support.Comment: 4 pages, 5 figure
A torque formula for non-isothermal Type I planetary migration - II. Effects of diffusion
We study the effects of diffusion on the non-linear corotation torque, or
horseshoe drag, in the two-dimensional limit, focusing on low-mass planets for
which the width of the horseshoe region is much smaller than the scale height
of the disc. In the absence of diffusion, the non-linear corotation torque
saturates, leaving only the Lindblad torque. Diffusion of heat and momentum can
act to sustain the corotation torque. In the limit of very strong diffusion,
the linear corotation torque is recovered. For the case of thermal diffusion,
this limit corresponds to having a locally isothermal equation of state. We
present some simple models that are able to capture the dependence of the
torque on diffusive processes to within 20% of the numerical simulations.Comment: 12 pages, 8 figures, accepted for publication in MNRA
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