9,470 research outputs found
Symmetric flows for compressible heat-conducting fluids with temperature dependent viscosity coefficients
We consider the Navier--Stokes equations for compressible heat-conducting
ideal polytropic gases in a bounded annular domain when the viscosity and
thermal conductivity coefficients are general smooth functions of temperature.
A global-in-time, spherically or cylindrically symmetric, classical solution to
the initial boundary value problem is shown to exist uniquely and converge
exponentially to the constant state as the time tends to infinity under certain
assumptions on the initial data and the adiabatic exponent . The
initial data can be large if is sufficiently close to 1. These results
are of Nishida--Smoller type and extend the work [Liu et al., SIAM J. Math.
Anal. 46 (2014), 2185--2228] restricted to the one-dimensional flows
Stability of stationary solutions to the outflow problem for full compressible Navier-Stokes equations with large initial perturbation
We investigate the large-time behavior of solutions to an outflow problem of
the full compressible Navier-Stokes equations in the half line. The
non-degenerate stationary solution is shown to be asymptotically stable under
large initial perturbation with no restriction on the adiabatic exponent
, provided that the boundary strength is sufficiently small. The proofs
are based on the standard energy method and the crucial step is to obtain
positive lower and upper bounds of the density and the temperature uniformly in
time and space.Comment: Contact [email protected] for any comment
Asymptotic stability of wave patterns to compressible viscous and heat-conducting gases in the half space
We study the large-time behavior of solutions to the compressible
Navier-Stokes equations for a viscous and heat-conducting ideal polytropic gas
in the one-dimensional half-space. A rarefaction wave and its superposition
with a non-degenerate stationary solution are shown to be asymptotically stable
for the outflow problem with large initial perturbation and general adiabatic
exponent.Comment: Contact [email protected] for any comments. arXiv admin note:
substantial text overlap with arXiv:1503.0392
Crystal Image Analysis based on Fast Synchrosqueezed Transforms
We propose an efficient algorithm to analyze atomic resolution crystal
images based on a fast synchrosqueezed wave packet transform. The proposed
algorithm can automatically extract microscopic information from atomic
resolution crystal images, e.g., crystal orientation, defects, and deformation,
which are important information for characterizing material properties. The
effectiveness of our algorithms is illustrated by experiments of synthetic
datasets and real D microscopic colloidal images
Mixed soliton solutions of the defocusing nonlocal nonlinear Schrodinger equation
By using the Darboux transformation, we obtain two new types of
exponential-and-rational mixed soliton solutions for the defocusing nonlocal
nonlinear Schrodinger equation. We reveal that the first type of solution can
display a large variety of interactions among two exponential solitons and two
rational solitons, in which the standard elastic interaction properties are
preserved and each soliton could be either the dark or antidark type. By
developing the asymptotic analysis technique, we also find that the second type
of solution can exhibit the elastic interactions among four mixed asymptotic
solitons. But in sharp contrast to the common solitons, the asymptotic mixed
solitons have the t-dependent velocities and their phase shifts before and
after interaction also grow with |t| in the logarithmical manner. In addition,
we discuss the degenerate cases for such two types of mixed soliton solutions
when the four-soliton interaction reduces to a three-soliton or two-soliton
interaction.Comment: 28 pages, 7 figure
Weighted approximate Fekete points: Sampling for least-squares polynomial approximation
We propose and analyze a weighted greedy scheme for computing deterministic
sample configurations in multidimensional space for performing least-squares
polynomial approximations on spaces weighted by a probability density
function. Our procedure is a particular weighted version of the approximate
Fekete points method, with the weight function chosen as the (inverse)
Christoffel function. Our procedure has theoretical advantages: when linear
systems with optimal condition number exist, the procedure finds them. In the
one-dimensional setting with any density function, our greedy procedure almost
always generates optimally-conditioned linear systems. Our method also has
practical advantages: our procedure is impartial to compactness of the domain
of approximation, and uses only pivoted linear algebraic routines. We show
through numerous examples that our sampling design outperforms competing
randomized and deterministic designs when the domain is both low and high
dimensional.Comment: 21 pages, 11 figure
Stochastic collocation methods via minimization using randomized quadratures
In this work, we discuss the problem of approximating a multivariate function
via minimization method, using a random chosen sub-grid of the
corresponding tensor grid of Gaussian points. The independent variables of the
function are assumed to be random variables, and thus, the framework provides a
non-intrusive way to construct the generalized polynomial chaos expansions,
stemming from the motivating application of Uncertainty Quantification (UQ). We
provide theoretical analysis on the validity of the approach. The framework
includes both the bounded measures such as the uniform and the Chebyshev
measure, and the unbounded measures which include the Gaussian measure. Several
numerical examples are given to confirm the theoretical results.Comment: 25 pages, 8 figure
M2Det: A Single-Shot Object Detector based on Multi-Level Feature Pyramid Network
Feature pyramids are widely exploited by both the state-of-the-art one-stage
object detectors (e.g., DSSD, RetinaNet, RefineDet) and the two-stage object
detectors (e.g., Mask R-CNN, DetNet) to alleviate the problem arising from
scale variation across object instances. Although these object detectors with
feature pyramids achieve encouraging results, they have some limitations due to
that they only simply construct the feature pyramid according to the inherent
multi-scale, pyramidal architecture of the backbones which are actually
designed for object classification task. Newly, in this work, we present a
method called Multi-Level Feature Pyramid Network (MLFPN) to construct more
effective feature pyramids for detecting objects of different scales. First, we
fuse multi-level features (i.e. multiple layers) extracted by backbone as the
base feature. Second, we feed the base feature into a block of alternating
joint Thinned U-shape Modules and Feature Fusion Modules and exploit the
decoder layers of each u-shape module as the features for detecting objects.
Finally, we gather up the decoder layers with equivalent scales (sizes) to
develop a feature pyramid for object detection, in which every feature map
consists of the layers (features) from multiple levels. To evaluate the
effectiveness of the proposed MLFPN, we design and train a powerful end-to-end
one-stage object detector we call M2Det by integrating it into the architecture
of SSD, which gets better detection performance than state-of-the-art one-stage
detectors. Specifically, on MS-COCO benchmark, M2Det achieves AP of 41.0 at
speed of 11.8 FPS with single-scale inference strategy and AP of 44.2 with
multi-scale inference strategy, which is the new state-of-the-art results among
one-stage detectors. The code will be made available on
\url{https://github.com/qijiezhao/M2Det.Comment: AAAI1
Systematic Construction of tight-binding Hamiltonians for Topological Insulators and Superconductors
A remarkable discovery in recent years is that there exist various kinds of
topological insulators and superconductors characterized by a periodic table
according to the system symmetry and dimensionality. To physically realize
these peculiar phases and study their properties, a critical step is to
construct experimentally relevant Hamiltonians which support these topological
phases. We propose a general and systematic method based on the quaternion
algebra to construct the tight binding Hamiltonians for all the
three-dimensional topological phases in the periodic table characterized by
arbitrary integer topological invariants, which include the spin-singlet and
the spin-triplet topological superconductors, the Hopf and the chiral
topological insulators as particular examples. For each class, we calculate the
corresponding topological invariants through both geometric analysis and
numerical simulation.Comment: 7 pages (including supplemental material), 1 figure, 1 tabl
Hamiltonian tomography for quantum many-body systems with arbitrary couplings
Characterization of qubit couplings in many-body quantum systems is essential
for benchmarking quantum computation and simulation. We propose a tomographic
measurement scheme to determine all the coupling terms in a general many-body
Hamiltonian with arbitrary long-range interactions, provided the energy density
of the Hamiltonian remains finite. Different from quantum process tomography,
our scheme is fully scalable with the number of qubits as the required rounds
of measurements increase only linearly with the number of coupling terms in the
Hamiltonian. The scheme makes use of synchronized dynamical decoupling pulses
to simplify the many-body dynamics so that the unknown parameters in the
Hamiltonian can be retrieved one by one. We simulate the performance of the
scheme under the influence of various pulse errors and show that it is robust
to typical noise and experimental imperfections.Comment: 9 pages, 4 figures, including supplemental materia
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