11,834 research outputs found
Primitive Cohomology of Hopf algebras
Primitive cohomology of a Hopf algebra is defined by using a modification of
the cobar construction of the underlying coalgebra. Among many of its
applications, two classifications are presented. Firstly we classify all non
locally PI, pointed Hopf algebra domains of Gelfand-Kirillov dimension two; and
secondly we classify all pointed Hopf algebras of rank one. The first
classification extends some results of Brown, Goodearl and others in an ongoing
project to understand all Hopf algebras of low Gelfand-Kirillov dimension. The
second generalizes results of Krop-Radford and Wang-You-Chen which classified
Hopf algebras of rank one under extra hypothesis. Properties and algebraic
structures of the primitive cohomology are discussed
Active optical clock based on four-level quantum system
Active optical clock, a new conception of atomic clock, has been proposed
recently. In this report, we propose a scheme of active optical clock based on
four-level quantum system. The final accuracy and stability of two-level
quantum system are limited by second-order Doppler shift of thermal atomic
beam. To three-level quantum system, they are mainly limited by light shift of
pumping laser field. These limitations can be avoided effectively by applying
the scheme proposed here. Rubidium atom four-level quantum system, as a typical
example, is discussed in this paper. The population inversion between
and states can be built up at a time scale of s.
With the mechanism of active optical clock, in which the cavity mode linewidth
is much wider than that of the laser gain profile, it can output a laser with
quantum-limited linewidth narrower than 1 Hz in theory. An experimental
configuration is designed to realize this active optical clock.Comment: 5 page
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Modeling and simulating of reservoir operation using the artificial neural network, support vector regression, deep learning algorithm
Reservoirs and dams are vital human-built infrastructures that play essential roles in flood control, hydroelectric power generation, water supply, navigation, and other functions. The realization of those functions requires efficient reservoir operation, and the effective controls on the outflow from a reservoir or dam. Over the last decade, artificial intelligence (AI) techniques have become increasingly popular in the field of streamflow forecasts, reservoir operation planning and scheduling approaches. In this study, three AI models, namely, the backpropagation (BP) neural network, support vector regression (SVR) technique, and long short-term memory (LSTM) model, are employed to simulate reservoir operation at monthly, daily, and hourly time scales, using approximately 30 years of historical reservoir operation records. This study aims to summarize the influence of the parameter settings on model performance and to explore the applicability of the LSTM model to reservoir operation simulation. The results show the following: (1) for the BP neural network and LSTM model, the effects of the number of maximum iterations on model performance should be prioritized; for the SVR model, the simulation performance is directly related to the selection of the kernel function, and sigmoid and RBF kernel functions should be prioritized; (2) the BP neural network and SVR are suitable for the model to learn the operation rules of a reservoir from a small amount of data; and (3) the LSTM model is able to effectively reduce the time consumption and memory storage required by other AI models, and demonstrate good capability in simulating low-flow conditions and the outflow curve for the peak operation period
Low-momentum Pion Enhancement Induced by Chiral Symmetry Restoration
The thermal and nonthermal pion production by sigma decay and its relation
with chiral symmetry restoration in a hot and dense matter are investigated.
The nonthermal decay into pions of sigma mesons which are popularly produced in
chiral symmetric phase leads to a low-momentum pion enhancement as a possible
signature of chiral phase transition at finite temperature and density.Comment: 3 pages, 2 figure
Patterns Formation in Drying Drops of Blood
The drying of a drop of human blood exhibits coupled physical mechanisms,
such as Marangoni flow, evaporation and wettability. The final stage of a whole
blood drop evaporation reveals regular patterns with a good reproducibility for
a healthy person. Other experiments on anaemic and hyperlipidemic people were
performed, and different patterns were revealed. The flow motion inside the
blood drop is observed and analyzed with the use of a digital camera: the
influence of the red blood cells (RBCs) motion is revealed at the drop
periphery as well as its consequences on the final stage of drying. The
mechanisms which lead to the final pattern of the dried blood drops are
presented and explained on the basis of fluid mechanics in conjunction with the
principles of haematology. The blood drop evaporation process is evidenced to
be driven only by Marangoni flow. The same axisymetric pattern formation is
observed, and can be forecast for different blood drop diameters. The
evaporation mass flux can be predicted with a good agreement, assuming only the
knowledge of the colloids mass concentration.Comment: 1 page + conference APS 2011 (1 movie for the gallery + 1 movie for
ArXiv
Thermal and Nonthermal Pion Enhancements with Chiral Symmetry Restoration
The pion production by sigma decay and its relation with chiral symmetry
restoration in a hot and dense matter are investigated in the framework of the
Nambu-Jona-Lasinio model. The decay rate for the process sigma -> 2pion to the
lowest order in a 1/N_c expansion is calculated as a function of temperature T
and chemical potential mu. The thermal and nonthermal enhancements of pions
generated by the decay before and after the freeze-out present only in the
crossover region of the chiral symmetry transition. The strongest nonthermal
enhancement is located in the vicinity of the endpoint of the first-order
transition.Comment: Latex2e, 12 pages, 8 Postscript figures, submitted to Phys. Rev.
Phase Diagram of Cold Polarized Fermi Gas in Two Dimensions
The superfluid phase diagrams of a two-dimensional cold polarized Fermi gas
in the BCS-BEC crossover are systematically and analytically investigated. In
the BCS-Leggett mean field theory, the transition from unpolarized superfluid
phase to normal phase is always of first order. For a homogeneous system, the
two critical Zeeman fields and the critical population imbalance are
analytically determined in the whole coupling parameter region, and the
superfluid-normal mixed phase is shown to be the ground state between the two
critical fields. The density profile in the presence of a harmonic trap
calculated in the local density approximation exhibits a shell structure, a
superfluid core at the center and a normal shell outside. For weak interaction,
the normal shell contains a partially polarized cloud with constant density
difference surrounded by a fully polarized state. For strong interaction, the
normal shell is totally in fully polarized state with a density profile
depending only on the global population imbalance. The di-fermion bound states
can survive in the whole highly imbalanced normal phase.Comment: V3: extended version according to referee's comment. 12 pages, 6
figures. Analytical results of density profile in trapped system are
reported; V4: Version accepted by Physical Review
An Analytic Solution of Hydrodynamic Equations with Source Terms in Heavy Ion Collisions
The energy and baryon densities in heavy ion collisions are estimated by
analytically solving a 1+1 dimensional hydrodynamical model with source terms.
Particularly, a competition between the energy and baryon sources and the
expansion of the system is discussed in detail.Comment: LaTeX2e, 7 pages, 4 postscript figures, submitted to Int. J. Mod.
Phys.
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