9,331 research outputs found
Nonlinear input-normal realizations based on the differential eigenstructure of hankel operators
This paper investigates the differential eigenstructure of Hankel operators for nonlinear systems. First, it is proven that the variational system and the Hamiltonian extension with extended input and output spaces can be interpreted as the GĂÂąteaux differential and its adjoint of a dynamical input-output system, respectively. Second, the GĂÂąteaux differential is utilized to clarify the main result the differential eigenstructure of the nonlinear Hankel operator which is closely related to the Hankel norm of the original system. Third, a new characterization of the nonlinear extension of Hankel singular values are given based on the differential eigenstructure. Finally, a balancing procedure to obtain a new input-normal/output-diagonal realization is derived. The results in this paper thus provide new insights to the realization and balancing theory for nonlinear systems.
Comment on `Equilibrium crystal shape of the Potts model at the first-order transition point'
We comment on the article by Fujimoto (1997 J. Phys. A: Math. Gen., Vol. 30,
3779), where the exact equilibrium crystal shape (ECS) in the critical Q-state
Potts model on the square lattice was calculated, and its equivalence with ECS
in the Ising model was established. We confirm these results, giving their
alternative derivation applying the transformation properties of the
one-particle dispersion relation in the six-vertex model. It is shown, that
this dispersion relation is identical with that in the Ising model on the
square lattice.Comment: 4 pages, 1 figure, LaTeX2
Balancing and model reduction for discrete-time nonlinear systems based on Hankel singular value analysis
This paper is concerned with balanced realization and model reduction for discrete-time nonlinear systems. Singular perturbation type balanced truncation method is proposed. In this procedure, the Hankel singular values and the related controllability and observability properties are preserved, which is a natural generalization of both the linear discrete-time case and the nonlinear continuous-time case.
Leading logarithm calculation of the e^+ e^- -> e^+ \nu_e \bar{u} d cross section
We analytically evaluate in the leading logarithm approximation the
differential cross section for e^+ e^- -> e^+ \nu_e \bar{u} d. We compare our
order \alpha^4 \alpha_s^0 leading-log result to the order \alpha^4 \alpha_s^0
exact result obtained from the GRC4F Monte Carlo program. Finally we use the
Gluck, Reya, Schienbien distribution of partons in a virtual photon, which
incorporates both evolution and nonperturbative strong interaction
contributions, to obtain better estimates of the differential cross section.Comment: 10 pages including 9 figure
A fundamental test for stellar feedback recipes in galaxy simulations
Direct comparisons between galaxy simulations and observations that both
reach scales < 100 pc are strong tools to investigate the cloud-scale physics
of star formation and feedback in nearby galaxies. Here we carry out such a
comparison for hydrodynamical simulations of a Milky Way-like galaxy, including
stochastic star formation, HII region and supernova feedback, and chemical
post-processing at 8 pc resolution. Our simulation shows excellent agreement
with almost all kpc-scale and larger observables, including total star
formation rates, radial profiles of CO, HI, and star formation through the
galactic disc, mass ratios of the ISM components, both whole-galaxy and
resolved Kennicutt-Schmidt relations, and giant molecular cloud properties.
However, we find that our simulation does not reproduce the observed
de-correlation between tracers of gas and star formation on < 100 pc scales,
known as the star formation 'uncertainty principle', which indicates that
observed clouds undergo rapid evolutionary lifecycles. We conclude that the
discrepancy is driven by insufficiently-strong pre-supernova feedback in our
simulation, which does not disperse the surrounding gas completely, leaving
star formation tracer emission too strongly associated with molecular gas
tracer emission, inconsistent with observations. This result implies that the
cloud-scale de-correlation of gas and star formation is a fundamental test for
feedback prescriptions in galaxy simulations, one that can fail even in
simulations that reproduce all other macroscopic properties of star-forming
galaxies.Comment: 13 pages, 10 figures, accepted for publication in MNRA
Suprathermal electrons at Saturn's bow shock
The leading explanation for the origin of galactic cosmic rays is particle
acceleration at the shocks surrounding young supernova remnants (SNRs),
although crucial aspects of the acceleration process are unclear. The similar
collisionless plasma shocks frequently encountered by spacecraft in the solar
wind are generally far weaker (lower Mach number) than these SNR shocks.
However, the Cassini spacecraft has shown that the shock standing in the solar
wind sunward of Saturn (Saturn's bow shock) can occasionally reach this
high-Mach number astrophysical regime. In this regime Cassini has provided the
first in situ evidence for electron acceleration under quasi-parallel upstream
magnetic conditions. Here we present the full picture of suprathermal electrons
at Saturn's bow shock revealed by Cassini. The downstream thermal electron
distribution is resolved in all data taken by the low-energy electron detector
(CAPS-ELS, <28 keV) during shock crossings, but the higher energy channels were
at (or close to) background. The high-energy electron detector (MIMI-LEMMS, >18
keV) measured a suprathermal electron signature at 31 of 508 crossings, where
typically only the lowest energy channels (<100 keV) were above background. We
show that these results are consistent with theory in which the "injection" of
thermal electrons into an acceleration process involves interaction with
whistler waves at the shock front, and becomes possible for all upstream
magnetic field orientations at high Mach numbers like those of the strong
shocks around young SNRs. A future dedicated study will analyze the rare
crossings with evidence for relativistic electrons (up to ~1 MeV).Comment: 22 pages, 5 figures. Accepted for publication in Ap
Transport Properties of the One Dimensional Ferromagnetic Kondo Lattice Model : A Qualitative Approach to Oxide Manganites
The transport properties of the ferromagnetic Kondo lattice model in one
dimension are studied via bosonization methods. The antiferromagnetic
fluctuations, which normally appear because of the RKKY interactions, are
explicitly taken into account as a direct exchange between the ``core'' spins.
It is shown that in the paramagnetic regime with the local antiferromagnetic
fluctuations, the resistivity decays exponentially as the temperature increases
while in the ferromagnetic regime the system is an almost perfect conductor. %A
non-perturbative description of localized spin polarons %in the paramagnetic
region is obtained.
The effect of a weak applied field is discussed to be reduced to the case of
the ferromagnetic state leading to band splitting. The qualitative relevance of
the results for the problem of the Oxide Manganites is emphasized.Comment: 4 pages, REVTe
Turbulent Mixing in the Surface Layers of Accreting Neutron Stars
During accretion a neutron star (NS) is spun up as angular momentum is
transported through its surface layers. We study the resulting differentially
rotating profile, focusing on the impact this has for type I X-ray bursts. The
predominant viscosity is likely provided by the Tayler-Spruit dynamo. The
radial and azimuthal magnetic field components have strengths of ~10^5 G and
~10^10 G, respectively. This leads to nearly uniform rotation at the depths of
interest for X-ray bursts. A remaining small shear transmits the accreted
angular momentum inward to the NS interior. Though this shear gives little
viscous heating, it can trigger turbulent mixing. Detailed simulations will be
required to fully understand the consequences of mixing, but our models
illustrate some general features. Mixing has the greatest impact when the
buoyancy at the compositional discontinuity between accreted matter and ashes
is overcome. This occurs at high accretion rates, at low spin frequencies, or
may depend on the ashes from the previous burst. We then find two new regimes
of burning. The first is ignition in a layer containing a mixture of heavier
elements from the ashes. If ignition occurs at the base of the mixed layer,
recurrence times as short as ~5-30 minutes are possible. This may explain the
short recurrence time of some bursts, but incomplete burning is still needed to
explain these bursts' energetics. When mixing is sufficiently strong, a second
regime is found where accreted helium mixes deep enough to burn stably,
quenching X-ray bursts. We speculate that the observed change in X-ray burst
properties near one-tenth the Eddington accretion rate is from this mechanism.
The carbon-rich material produced by stable helium burning would be important
for triggering and fueling superbursts. (abridged)Comment: Accepted for publication in The Astrophysical Journal, 16 pages, 15
figure
Automatic one-loop calculation of MSSM processes with GRACE
We have developed the system for the automatic computation of cross-sections,
{\tt GRACE/SUSY}, including the one-loop calculations for processes of the
minimal supersymmetric extension of the the standard model. For an application,
we investigate the process .Comment: 4 pages, 1 figure, Talk presented by Jimbo, M. at ACAT-0
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