41,160 research outputs found
Computing the lower and upper bounds of Laplace eigenvalue problem: by combining conforming and nonconforming finite element methods
This article is devoted to computing the lower and upper bounds of the
Laplace eigenvalue problem. By using the special nonconforming finite elements,
i.e., enriched Crouzeix-Raviart element and extension , we get
the lower bound of the eigenvalue. Additionally, we also use conforming finite
elements to do the postprocessing to get the upper bound of the eigenvalue. The
postprocessing method need only to solve the corresponding source problems and
a small eigenvalue problem if higher order postprocessing method is
implemented. Thus, we can obtain the lower and upper bounds of the eigenvalues
simultaneously by solving eigenvalue problem only once. Some numerical results
are also presented to validate our theoretical analysis.Comment: 19 pages, 4 figure
Gamma-Ray Bursts are Produced Predominately in the Early Universe
It is known that some observed gamma-ray bursts (GRBs) are produced at
cosmological distances and that the GRB production rate may follow the star
formation rate. We model the BATSE-detected intensity distribution of long GRBs
in order to determine their space density distribution and opening angle
distribution. Our main results are: the lower and upper distance limits to the
GRB production are z 0.24 and >10, respectively; the GRB opening angle follows
an exponential distribution and the mean opening angle is about 0.03 radians;
and the peak luminosity appears to be a better standard candle than the total
energy of a GRB.Comment: 12 pages, 2 figur
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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
Concerning the Motion and Orientation of Flux Transfer Events Produced by Component and Antiparallel Reconnection
We employ the Cooling et al. (2001) model to predict the location, orientation, motion, and signatures of flux transfer events (FTEs) generated at the solstices and equinoxes along extended subsolar component and high ]latitude antiparallel reconnection curves for typical solar wind plasma conditions and various interplanetary magnetic field (IMF) strengths and directions. In general, events generated by the two mechanisms maintain the strikingly different orientations they begin with as they move toward the terminator in opposite pairs of magnetopause quadrants. The curves along which events generated by component reconnection form bow toward the winter cusp. Events generated by antiparallel reconnection form on the equatorial magnetopause during intervals of strongly southward IMF orientation during the equinoxes, form in the winter hemisphere and only reach the dayside equatorial magnetopause during the solstices when the IMF strength is very large and the IMF points strongly southward, never reach the equatorial dayside magnetopause when the IMF has a substantial dawnward or duskward component, and never reach the equatorial flank magnetopause during intervals of northward and dawnward or duskward IMF orientation. Magnetosheath magnetic fields typically have strong components transverse to events generated by component reconnection but only weak components transverse to the axes of events generated by antiparallel reconnection. As a result, much stronger bipolar magnetic field signatures normal to the nominal magnetopause should accompany events generated by component reconnection. The results presented in this paper suggest that events generated by component reconnection predominate on the dayside equatorial and flank magnetopause for most solar wind conditions
Fractional Quantum Hall Effect of Hard-Core Bosons in Topological Flat Bands
Recent proposals of topological flat band (TFB) models have provided a new
route to realize the fractional quantum Hall effect (FQHE) without Landau
levels. We study hard-core bosons with short-range interactions in two
representative TFB models, one of which is the well known Haldane model (but
with different parameters). We demonstrate that FQHE states emerge with
signatures of even number of quasi-degenerate ground states on a torus and a
robust spectrum gap separating these states from higher energy spectrum. We
also establish quantum phase diagrams for the filling factor 1/2 and illustrate
quantum phase transitions to other competing symmetry-breaking phases.Comment: 4 pages, 6 figure
Time evolution, cyclic solutions and geometric phases for general spin in an arbitrarily varying magnetic field
A neutral particle with general spin and magnetic moment moving in an
arbitrarily varying magnetic field is studied. The time evolution operator for
the Schr\"odinger equation can be obtained if one can find a unit vector that
satisfies the equation obeyed by the mean of the spin operator. There exist at
least cyclic solutions in any time interval. Some particular time
interval may exist in which all solutions are cyclic. The nonadiabatic
geometric phase for cyclic solutions generally contains extra terms in addition
to the familiar one that is proportional to the solid angle subtended by the
closed trace of the spin vector.Comment: revtex4, 8 pages, no figur
TimeMachine: Timeline Generation for Knowledge-Base Entities
We present a method called TIMEMACHINE to generate a timeline of events and
relations for entities in a knowledge base. For example for an actor, such a
timeline should show the most important professional and personal milestones
and relationships such as works, awards, collaborations, and family
relationships. We develop three orthogonal timeline quality criteria that an
ideal timeline should satisfy: (1) it shows events that are relevant to the
entity; (2) it shows events that are temporally diverse, so they distribute
along the time axis, avoiding visual crowding and allowing for easy user
interaction, such as zooming in and out; and (3) it shows events that are
content diverse, so they contain many different types of events (e.g., for an
actor, it should show movies and marriages and awards, not just movies). We
present an algorithm to generate such timelines for a given time period and
screen size, based on submodular optimization and web-co-occurrence statistics
with provable performance guarantees. A series of user studies using Mechanical
Turk shows that all three quality criteria are crucial to produce quality
timelines and that our algorithm significantly outperforms various baseline and
state-of-the-art methods.Comment: To appear at ACM SIGKDD KDD'15. 12pp, 7 fig. With appendix. Demo and
other info available at http://cs.stanford.edu/~althoff/timemachine
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