211,915 research outputs found
Solitary Waves Bifurcated from Bloch Band Edges in Two-dimensional Periodic Media
Solitary waves bifurcated from edges of Bloch bands in two-dimensional
periodic media are determined both analytically and numerically in the context
of a two-dimensional nonlinear Schr\"odinger equation with a periodic
potential. Using multi-scale perturbation methods, envelope equations of
solitary waves near Bloch bands are analytically derived. These envelope
equations reveal that solitary waves can bifurcate from edges of Bloch bands
under either focusing or defocusing nonlinearity, depending on the signs of
second-order dispersion coefficients at the edge points. Interestingly, at edge
points with two linearly independent Bloch modes, the envelope equations lead
to a host of solitary wave structures including reduced-symmetry solitons,
dipole-array solitons, vortex-cell solitons, and so on -- many of which have
never been reported before. It is also shown analytically that the centers of
envelope solutions can only be positioned at four possible locations at or
between potential peaks. Numerically, families of these solitary waves are
directly computed both near and far away from band edges. Near the band edges,
the numerical solutions spread over many lattice sites, and they fully agree
with the analytical solutions obtained from envelope equations. Far away from
the band edges, solitary waves are strongly localized with intensity and phase
profiles characteristic of individual families.Comment: 23 pages, 15 figures. To appear in Phys. Rev.
Existence of Multistring Solutions of the Self-Gravitating Massive Boson
We consider a semilinear elliptic system which include the model system of
the strings in the cosmology as a special case. We prove existence of
multi-string solutions and obtain precise asymptotic decay estimates near
infinity for the solutions.
As a special case of this result we solve an open problem posed in
\cite{yan}Comment: 12 page
A Pecking Order Analysis of Graduate Overeducation and Educational Investment in China
Against the background of the recent rate of expansion of China's higher education system that has outstripped even China's own high rate of economic growth, the paper examines evidence of the emerging problem of graduate overeducation within China. Based upon a pecking-order model of employment offers and associated ordered probit model, it analyses the empirical factors which determine the incidence of graduate overeducation across China. The extent to which individual students have an incentive to become overeducated compared to a socially optimal level of their education is also examined in the context of a supporting economic model that compares individual and socially optimal levels of investment in education, in the face of labour market demands. The extent of the divergence between individual and socially optimal levels of investment in education, and of the associated levels of graduate overeducation, is found to depend upon how recent major increases in the supply of graduates within China will interact with the future growth rates in job specifications, in demand variables and in resultant graduate wages within China.Graduate overeducation. higher education policy. Optimal education investment. Economic growth in China
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Operational solar forecasting for the real-time market
Despite the significant progress made in solar forecasting over the last decade, most of the proposed models cannot be readily used by independent system operators (ISOs). This article proposes an operational solar forecasting algorithm that is closely aligned with the real-time market (RTM) forecasting requirements of the California ISO (CAISO). The algorithm first uses the North American Mesoscale (NAM) forecast system to generate hourly forecasts for a 5-h period that are issued 12 h before the actual operating hour, satisfying the lead-time requirement. Subsequently, the world's fastest similarity search algorithm is adopted to downscale the hourly forecasts generated by NAM to a 15-min resolution, satisfying the forecast-resolution requirement. The 5-h-ahead forecasts are repeated every hour, following the actual rolling update rate of CAISO. Both deterministic and probabilistic forecasts generated using the proposed algorithm are empirically evaluated over a period of 2 years at 7 locations in 5 climate zones
The ground state and the long-time evolution in the CMC Einstein flow
Let (g,K)(k) be a CMC (vacuum) Einstein flow over a compact three-manifold M
with non-positive Yamabe invariant (Y(M)). As noted by Fischer and Moncrief,
the reduced volume V(k)=(-k/3)^{3}Vol_{g(k)}(M) is monotonically decreasing in
the expanding direction and bounded below by V_{\inf}=(-1/6)Y(M))^{3/2}.
Inspired by this fact we define the ground state of the manifold M as "the
limit" of any sequence of CMC states {(g_{i},K_{i})} satisfying: i. k_{i}=-3,
ii. V_{i} --> V_{inf}, iii. Q_{0}((g_{i},K_{i}))< L where Q_{0} is the
Bel-Robinson energy and L is any arbitrary positive constant. We prove that (as
a geometric state) the ground state is equivalent to the Thurston
geometrization of M. Ground states classify naturally into three types. We
provide examples for each class, including a new ground state (the Double Cusp)
that we analyze in detail. Finally consider a long time and cosmologically
normalized flow (\g,\K)(s)=((-k/3)^{2}g,(-k/3))K) where s=-ln(-k) is in
[a,\infty). We prove that if E_{1}=E_{1}((\g,\K))< L (where E_{1}=Q_{0}+Q_{1},
is the sum of the zero and first order Bel-Robinson energies) the flow
(\g,\K)(s) persistently geometrizes the three-manifold M and the geometrization
is the ground state if V --> V_{inf}.Comment: 40 pages. This article is an improved version of the second part of
the First Version of arXiv:0705.307
Single/Few Bunch Space Charge Effects at 8-GeV in the Fermilab Main Injector
For Project X, it is planned to inject a beam of 3x10**11 particles per bunch
into the Main Injector. Therefore, at 8-GeV, there will be increased space
charge tune shifts and an increased incoherent tune spread. In preparation for
these higher intensity bunches exploratory studies have commenced looking at
the transmission of different intensity bunches at different tunes. An
experiment is described with results for bunch intensities between 20 and 300
10**9 particles. To achieve the highest intensity bunches coalescing at 8-GeV
is required, resulting in a longer bunch length. Comparisons show that similar
transmission curves are obtained when the intensity and bunch length have
increased by factors of 3.2 and 3.4 respectively, indicating the incoherent
tune shifts are similar, as expected from theory. The results of these
experiments will be used in conjugation with simulations to further study high
intensity bunches in the Main Injector.Comment: 3 pp. 3rd International Particle Accelerator Conference (IPAC 2012)
20-25 May 2012, New Orleans, Louisian
Pulling hairpinned polynucleotide chains: Does base-pair stacking interaction matter?
Force-induced structural transitions both in relatively random and in
designed single-stranded DNA (ssDNA) chains are studied theoretically. At high
salt conditions, ssDNA forms compacted hairpin patterns stabilized by
base-pairing and base-pair stacking interactions, and a threshold external
force is needed to pull the hairpinned structure into a random coiled one. The
base-pair stacking interaction in the ssDNA chain makes this hairpin-coil
conversion a discontinuous (first-order) phase transition process characterized
by a force plateau in the force-extension curve, while lowering this potential
below some critical level turns this transition into continuous (second-order)
type, no matter how strong the base-pairing interaction is. The phase diagram
(including hairpin-I, -II, and random coil) is discussed as a function of
stacking potential and external force. These results are in quantitative
agreement with recent experimental observations of different ssDNA sequences,
and they reveal the necessity to consider the base-pair stacking interactions
in order to understand the structural formation of RNA, a polymer designed by
nature itself. The theoretical method used may be extended to study the
long-range interaction along double-stranded DNA caused by the topological
constraint of fixed linking number.Comment: 8 pages using Revte
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