276,718 research outputs found
Resonant Interactions in Rotating Homogeneous Three-dimensional Turbulence
Direct numerical simulations of three-dimensional (3D) homogeneous turbulence
under rapid rigid rotation are conducted to examine the predictions of resonant
wave theory for both small Rossby number and large Reynolds number. The
simulation results reveal that there is a clear inverse energy cascade to the
large scales, as predicted by 2D Navier-Stokes equations for resonant
interactions of slow modes. As the rotation rate increases, the
vertically-averaged horizontal velocity field from 3D Navier-Stokes converges
to the velocity field from 2D Navier-Stokes, as measured by the energy in their
difference field. Likewise, the vertically-averaged vertical velocity from 3D
Navier-Stokes converges to a solution of the 2D passive scalar equation. The
energy flux directly into small wave numbers in the plane from
non-resonant interactions decreases, while fast-mode energy concentrates closer
to that plane. The simulations are consistent with an increasingly dominant
role of resonant triads for more rapid rotation
Comparison of the Geometrical Characters Inside Quark- and Gluon-jet Produced by Different Flavor Quarks
The characters of the angular distributions of quark jets and gluon jets with
different flavors are carefully studied after introducing the cone angle of
jets. The quark jets and gluon jets are identified from the 3-jet events which
are produced by Monte Carlo simulation Jetset7.4 in e+e- collisions at =91.2GeV. It turns out that the ranges of angular distributions of gluon jets
are obviously wider than that of quark jets at the same energies. The average
cone angles of gluon jets are much larger than that of quark jets. As the
multiplicity or the transverse momentum increases, the cone-angle distribution
without momentum weight of both the quark jet and gluon jet all increases, i.e
the positive linear correlation are present, but the cone-angle distribution
with momentum weight decreases at first, then increases when n > 4 or p_t > 2
GeV. The characters of cone angular distributions of gluon jets produced by
quarks with different flavors are the same, while there are obvious differences
for that of the quark jets with different flavors.Comment: 13 pages, 6 figures, to be published on the International Journal of
Modern Physics
Applications of diffraction theory to aeroacoustics
A review is given of the fundamentals of diffraction theory and the application of the theory to several problems of aircraft noise generation, propagation, and measurement. The general acoustic diffraction problem is defined and the governing equations set down. Diffraction phenomena are illustrated using the classical problem of the diffraction of a plane wave by a half-plane. Infinite series and geometric acoustic methods for solving diffraction problems are described. Four applications of diffraction theory are discussed: the selection of an appropriate shape for a microphone, the use of aircraft wings to shield the community from engine noise, the reflection of engine noise from an aircraft fuselage and the radiation of trailing edge noise
Classical Trajectory Perspective on Double Ionization Dynamics of Diatomic Molecules Irradiated by Ultrashort Intense Laser Pulses
In the present paper, we develop a semiclassical quasi-static model
accounting for molecular double ionization in an intense laser pulse. With this
model, we achieve insight into the dynamics of two highly-correlated valence
electrons under the combined influence of a two-center Coulomb potential and an
intense laser field, and reveal the significant influence of molecular
alignment on the ratio of double over single ion yield. Analysis on the
classical trajectories unveils sub-cycle dynamics of the molecular double
ionization. Many interesting features, such as the accumulation of emitted
electrons in the first and third quadrants of parallel momentum plane, the
regular pattern of correlated momentum with respect to the time delay between
closest collision and ionization moment, are revealed and successfully
explained by back analyzing the classical trajectories. Quantitative agreement
with experimental data over a wide range of laser intensities from tunneling to
over-the-barrier regime is presented.Comment: 8 pages, 9 figure
Time delays and energy transport velocities in three dimensional ideal cloaking
We obtained the energy transport velocity distribution for a three
dimensional ideal cloak explicitly. Near the operation frequency, the energy
transport velocity has rather peculiar distribution. The velocity along a line
joining the origin of the cloak is a constant, while the velocity approaches
zero at the inner boundary of the cloak. A ray pointing right into the origin
of the cloak will experience abrupt changes of velocities when it impinges on
the inner surface of the cloak. This peculiar distribution causes infinite time
delays for the ideal cloak within a geometric optics description.Comment: A scaling factor is added to convert the parameter \tau into the
physical tim
Expanded mixed multiscale finite element methods and their applications for flows in porous media
We develop a family of expanded mixed Multiscale Finite Element Methods
(MsFEMs) and their hybridizations for second-order elliptic equations. This
formulation expands the standard mixed Multiscale Finite Element formulation in
the sense that four unknowns (hybrid formulation) are solved simultaneously:
pressure, gradient of pressure, velocity and Lagrange multipliers. We use
multiscale basis functions for the both velocity and gradient of pressure. In
the expanded mixed MsFEM framework, we consider both cases of separable-scale
and non-separable spatial scales. We specifically analyze the methods in three
categories: periodic separable scales, - convergence separable scales, and
continuum scales. When there is no scale separation, using some global
information can improve accuracy for the expanded mixed MsFEMs. We present
rigorous convergence analysis for expanded mixed MsFEMs. The analysis includes
both conforming and nonconforming expanded mixed MsFEM. Numerical results are
presented for various multiscale models and flows in porous media with shales
to illustrate the efficiency of the expanded mixed MsFEMs.Comment: 33 page
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The application of Han Dynasty cultural elements to modern product design
Chinese Han Culture, as Chinese nation's "core culture", is the cultural symbol of Chinese nation, and played an important role in the history of Chinese cultural development, even in the history of world cultural development. Designing in the Han Dynasty, while inheriting Chinese traditional culture, but also having its unique style, are appreciated and respected by the people nowadays. In a modern society where the design is becoming more diversified, the innovative design based on traditional culture and art has its unique charm and vitality. This paper presented our recent research on the application of Han Dynasty cultural elements to modern product design, reflected the local design connotation of Han Dynasty cultural elements
Analysis of a Classical Matrix Preconditioning Algorithm
We study a classical iterative algorithm for balancing matrices in the
norm via a scaling transformation. This algorithm, which goes back
to Osborne and Parlett \& Reinsch in the 1960s, is implemented as a standard
preconditioner in many numerical linear algebra packages. Surprisingly, despite
its widespread use over several decades, no bounds were known on its rate of
convergence. In this paper we prove that, for any irreducible (real
or complex) input matrix~, a natural variant of the algorithm converges in
elementary balancing operations, where
measures the initial imbalance of~ and is the target imbalance
of the output matrix. (The imbalance of~ is , where
are the maximum entries in magnitude in the
th row and column respectively.) This bound is tight up to the
factor. A balancing operation scales the th row and column so that their
maximum entries are equal, and requires arithmetic operations on
average, where is the number of non-zero elements in~. Thus the running
time of the iterative algorithm is . This is the first time
bound of any kind on any variant of the Osborne-Parlett-Reinsch algorithm. We
also prove a conjecture of Chen that characterizes those matrices for which the
limit of the balancing process is independent of the order in which balancing
operations are performed.Comment: The previous version (1) (see also STOC'15) handled UB ("unique
balance") input matrices. In this version (2) we extend the work to handle
all input matrice
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