117,308 research outputs found
A Bi-Hamiltonian Formulation for Triangular Systems by Perturbations
A bi-Hamiltonian formulation is proposed for triangular systems resulted by
perturbations around solutions, from which infinitely many symmetries and
conserved functionals of triangular systems can be explicitly constructed,
provided that one operator of the Hamiltonian pair is invertible. Through our
formulation, four examples of triangular systems are exhibited, which also show
that bi-Hamiltonian systems in both lower dimensions and higher dimensions are
many and varied. Two of four examples give local 2+1 dimensional bi-Hamiltonian
systems and illustrate that multi-scale perturbations can lead to
higher-dimensional bi-Hamiltonian systems.Comment: 16 pages, to appear in J. Math. Phy
A refined invariant subspace method and applications to evolution equations
The invariant subspace method is refined to present more unity and more
diversity of exact solutions to evolution equations. The key idea is to take
subspaces of solutions to linear ordinary differential equations as invariant
subspaces that evolution equations admit. A two-component nonlinear system of
dissipative equations was analyzed to shed light on the resulting theory, and
two concrete examples are given to find invariant subspaces associated with
2nd-order and 3rd-order linear ordinary differential equations and their
corresponding exact solutions with generalized separated variables.Comment: 16 page
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Study on SPH Viscosity Term Formulations
For viscosity-dominated flows, the viscous effect plays a much more important role. Since the viscosity term in SPH-governing (Smoothed Particle Hydrodynamics) equations involves the discretization of a second-order derivative, its treatment could be much more challenging than that of a first-order derivative, such as the pressure gradient. The present paper summarizes a series of improved methods for modeling the second-order viscosity force term. By using a benchmark patch test, the numerical accuracy and efficiency of different approaches are evaluated under both uniform and non-uniform particle configurations. Then these viscosity force models are used to compute a documented lid-driven cavity flow and its interaction with a cylinder, from which the most recommended viscosity term formulation has been identified
Extension of Hereditary Symmetry Operators
Two models of candidates for hereditary symmetry operators are proposed and
thus many nonlinear systems of evolution equations possessing infinitely many
commutative symmetries may be generated. Some concrete structures of hereditary
symmetry operators are carefully analyzed on the base of the resulting general
conditions and several corresponding nonlinear systems are explicitly given out
as illustrative examples.Comment: 13 pages, LaTe
Transverse Momentum Dependent Factorization for Quarkonium Production at Low Transverse Momentum
Quarkonium production in hadron collisions at low transverse momentum
with as the quarkonium mass can be used for probing
transverse momentum dependent (TMD) gluon distributions. For this purpose, one
needs to establish the TMD factorization for the process. We examine the
factorization at the one-loop level for the production of or .
The perturbative coefficient in the factorization is determined at one-loop
accuracy. Comparing the factorization derived at tree level and that beyond the
tree level, a soft factor is, in general, needed to completely cancel soft
divergences. We have also discussed possible complications of TMD factorization
of p-wave quarkonium production.Comment: Title changed in the journal, published versio
Breakdown of QCD Factorization for P-Wave Quarkonium Production at Low Transverse Momentum
Quarkonium production at low transverse momentum in hadron collisions can be
used to extract Transverse-Momentum-Dependent(TMD) gluon distribution
functions, if TMD factorization holds there. We show that TMD factorization for
the case of P-wave quarkonium with holds at one-loop
level, but is violated beyond one-loop level. TMD factorization for other
P-wave quarkonium is also violated already at one-loop.Comment: Published version in Physics Letters B (2014), pp. 103-10
Constrained structure of ancient Chinese poetry facilitates speech content grouping
Ancient Chinese poetry is constituted by structured language that deviates from ordinary language usage [1, 2]; its poetic genres impose unique combinatory constraints on linguistic elements [3]. How does the constrained poetic structure facilitate speech segmentation when common linguistic [4, 5, 6, 7, 8] and statistical cues [5, 9] are unreliable to listeners in poems? We generated artificial Jueju, which arguably has the most constrained structure in ancient Chinese poetry, and presented each poem twice as an isochronous sequence of syllables to native Mandarin speakers while conducting magnetoencephalography (MEG) recording. We found that listeners deployed their prior knowledge of Jueju to build the line structure and to establish the conceptual flow of Jueju. Unprecedentedly, we found a phase precession phenomenon indicating predictive processes of speech segmentation—the neural phase advanced faster after listeners acquired knowledge of incoming speech. The statistical co-occurrence of monosyllabic words in Jueju negatively correlated with speech segmentation, which provides an alternative perspective on how statistical cues facilitate speech segmentation. Our findings suggest that constrained poetic structures serve as a temporal map for listeners to group speech contents and to predict incoming speech signals. Listeners can parse speech streams by using not only grammatical and statistical cues but also their prior knowledge of the form of language
New Lepton Family Symmetry and Neutrino Tribimaximal Mixing
The newly proposed finite symmetry Sigma(81) is applied to the problem of
neutrino tribimaximal mixing. The result is more satisfactory than those of
previous models based on A_4 in that the use of auxiliary symmetries (or
mechanisms) may be avoided. Deviations from the tribimaximal pattern are
expected, but because of its basic structure, only tan^2 (theta_12) may differ
significantly from 0.5 (say 0.45) with sin^2 (2 theta_23) remaining very close
to one, and theta_13 very nearly zero.Comment: 8 pages, no figur
Effect of polymer concentration and length of hydrophobic end block on the unimer-micelle transition broadness in amphiphilic ABA symmetric triblock copolymer solutions
The effects of the length of each hydrophobic end block N_{st} and polymer
concentration \bar{\phi}_{P} on the transition broadness in amphiphilic ABA
symmetric triblock copolymer solutions are studied using the self-consistent
field lattice model. When the system is cooled, micelles are observed, i.e.,the
homogenous solution (unimer)-micelle transition occurs. When N_{st} is
increased, at fixed \bar{\phi}_{P}, micelles occur at higher temperature, and
the temperature-dependent range of micellar aggregation and half-width of
specific heat peak for unimer-micelle transition increase monotonously.
Compared with associative polymers, it is found that the magnitude of the
transition broadness is determined by the ratio of hydrophobic to hydrophilic
blocks, instead of chain length. When \bar{\phi}_{P} is decreased, given a
large N_{st}, the temperature-dependent range of micellar aggregation and
half-width of specific heat peak initially decease, and then remain nearly
constant. It is shown that the transition broadness is concerned with the
changes of the relative magnitudes of the eductions of nonstickers and solvents
from micellar cores.Comment: 8 pages, 4 figure
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