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 $\gamma$. The initial data can be large if $\gamma$ 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 $\gamma$, 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

3D3D Crystal Image Analysis based on Fast Synchrosqueezed Transforms

We propose an efficient algorithm to analyze $3D$ atomic resolution crystal images based on a fast $3D$ synchrosqueezed wave packet transform. The proposed algorithm can automatically extract microscopic information from $3D$ 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 $3$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 $L^2$ 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 L1L_1 minimization using randomized quadratures

In this work, we discuss the problem of approximating a multivariate function via $\ell_1$ 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