arXiv subjects

Lijun Yang

Publications and source records attributed to Lijun Yang.

31 records · Page 2Linked to original sources

arXiv2022

Theoretical analysis of sound propagation and entropy generation across a distributed steady heat source

Acoustic and entropy waves interacting in a duct with a steady heat source and mean flow are analysed using an asymptotic expansion (AE) for low frequencies. The analytical AE solutions are obtained by taking advantage of flow invariants and applying a multi-step strategy. The proposed solutions provide first-order corrections to the compact model in the form of integrals of mean flow variables. An eigenvalue system is then built to predict the thermoacoustic modes of a duct containing a distributed heat source or sink. Predictions from the AE solutions agree well with the numerical results of the linearised Euler equations for both frequencies and growth rates, as long as the low-frequency condition is satisfied. The AE solutions are able to accurately reconstruct the acoustic and entropy waves and correct the significant errors in the predicted entropy wave associated with the compact model. The analysis illustrates that the thermoacoustic system needs to account for the entropy wave generated by the interaction of acoustic wave and the distributed steady heat source, especially when density- or entropy-dependent boundary conditions are prescribed at the duct ends. Furthermore, a combination of the AE method and the modified WKB approximation method is discussed for a cooling case. The AE solutions remedy the disadvantage of the WKB solution in the low and very low-frequency domain and facilitate full-frequency theoretical analyses of sound propagation and entropy generation in inhomogeneous duct flow fields.

physics.flu-dyn↗

arXiv2021

MHD Flow Regimes in Annular Channel

One method and two results are contributed to the complete understanding about MHD laminar flow in annular channel with transverse magnetic field in this paper. In terms of the method, a computationally cheap semi-analytic algorithm is developed based on spectral method and perturbation expansion. By virtue of the fast computation, dense cases with almost continuous varying Hartmann number $M$, Reynolds number $Re$ and cross-section ratio $η$ are calculated to explore the flow patterns that are missed in previous research. In terms of the results of inertialess regime, we establish the average velocity map and electric-flow coupling delimitation in $η$-$M$ space. Seven phenomenological flow patterns and their analytical approaches are identified. In terms of the results of inertial regime, we examine the law of decreasing order-of-magnitude of inertial perturbation on primary flow with increasing Hartmann number. The proposed semi-analytic solution coincides with the $Re^2/M^{4}$ suppression theory of Baylis & Hunt (J. Fluid Mech., vol. 43, 1971, pp. 423-428) in the case of $M<40$. When $M>40$, the pair of trapezoid vortices of secondary flow begins to crack and there is therefore a faster drop in inertial perturbation as $Re^2/M^{5}$, which is a new suppression theory. When $M>80$, the anomalous reverse vortices are fully developed near Shercliff layers resulting in the slower suppression mode of $Re^2/M^{2.5}$, which confirms the prediction of Tabeling & Chabrerie (J. Fluid Mech., vol. 103, 1981, pp. 225-239).

physics.flu-dyn↗

arXiv2019

An Integrated Inverse Space Sparse Representation Framework for Tumor Classification

Microarray gene expression data-based tumor classification is an active and challenging issue. In this paper, an integrated tumor classification framework is presented, which aims to exploit information in existing available samples, and focuses on the small sample problem and unbalanced classification problem. Firstly, an inverse space sparse representation based classification (ISSRC) model is proposed by considering the characteristics of gene-based tumor data, such as sparsity and a small number of training samples. A decision information factors (DIF)-based gene selection method is constructed to enhance the representation ability of the ISSRC. It is worth noting that the DIF is established from reducing clinical misdiagnosis rate and dimension of small sample data. For further improving the representation ability and classification stability of the ISSRC, feature learning is conducted on the selected gene subset. The feature learning method is constructed by complementing the advantages of non-negative matrix factorization (NMF) and deep learning. Without confusion, the ISSRC combined with gene selection and feature learning is called the integrated ISSRC, whose stability, optimization and the corresponding convergence are analyzed. Extensive experiments on six public microarray gene expression datasets show the integrated ISSRC-based tumor classification framework is superior to classical and state-of-the-art methods. There are significant improvements in classification accuracy, specificity and sensitivity, whether there is a tumor in the early diagnosis, what kind of tumor, or whether metastasis occurs after tumor surgery.

cs.CV↗

arXiv2017

Limit cycles by perturbing quadratic isochronous centers inside piecewise smooth polynomial differential systems

In the present paper, we study the number of zeros of the first order Melnikov function for piecewise smooth polynomial differential system, to estimate the number of limit cycles bifurcated from the period annulus of quadratic isochronous centers, when they are perturbed inside the class of all piecewise smooth polynomial differential systems of degree $n$ with the straight line of discontinuity $x=0$. An explicit and fairly accurate upper bound for the number of zeros of the first order Melnikov functions with respect to quadratic isochronous centers $S_1, S_2$ and $S_3$ is provided. For quadratic isochronous center $S_4$, we give a rough estimate for the number of zeros of the first order Melnikov function due to its complexity. Furthermore, we improve the upper bound associated with $S_4$, from $14n+11$ in \cite{LLLZ}, $12n-1$ in \cite{SZ} to $[(5n-5)/2]$, when it is perturbed inside all smooth polynomial differential systems of degree $n$. Besides, some evidence on the equivalence of the first order Melnikov function and the first order Averaged function for piecewise smooth polynomial differential systems is found.

math.CA↗

arXiv2017

Interaction-induced Bloch Oscillation in a Harmonically Trapped and Fermionized Quantum Gas in One Dimension

Motivated by a recent experiment by F. Meinert et al, arxiv:1608.08200, we study the dynamics of an impurity moving in the background of a harmonically trapped one-dimensional Bose gas in the hard-core limit. We show that due to the hidden "lattice" structure of background bosons, the impurity effectively feels a quasi-periodic potential via impurity-boson interactions that can drive the Bloch oscillation under an external force, even in the absence of real lattice potentials. Meanwhile, the inhomogeneous density of trapped bosons imposes an additional harmonic potential to the impurity, resulting in a similar oscillation dynamics but with different periods and amplitudes. We show that the sign and the strength of impurity-boson coupling can significantly affect above two potentials so as to determine the impurity dynamics.

cond-mat.quant-gas↗

arXiv2016

Extend natural neighbor: a novel classification method with self-adaptive neighborhood parameters in different stages

Various kinds of k-nearest neighbor (KNN) based classification methods are the bases of many well-established and high-performance pattern-recognition techniques, but both of them are vulnerable to their parameter choice. Essentially, the challenge is to detect the neighborhood of various data sets, while utterly ignorant of the data characteristic. This article introduces a new supervised classification method: the extend natural neighbor (ENaN) method, and shows that it provides a better classification result without choosing the neighborhood parameter artificially. Unlike the original KNN based method which needs a prior k, the ENaNE method predicts different k in different stages. Therefore, the ENaNE method is able to learn more from flexible neighbor information both in training stage and testing stage, and provide a better classification result.

cs.AI↗

arXiv2016

Bethe States of the integrable spin-s chain with generic open boundaries

Based on the inhomogeneous T-Q relation and the associated Bethe Ansatz equations obtained via the off-diagonal Bethe Ansatz, we construct the Bethe-type eigenstates of the SU(2)-invariant spin-s chain with generic non-diagonal boundaries by employing certain orthogonal basis of the Hilbert space.

math-ph↗

arXiv2016

Engineering quantum magnetism in one-dimensional trapped Fermi gases with p-wave interactions

The highly controllable ultracold atoms in a one-dimensional (1D) trap provide a new platform for the ultimate simulation of quantum magnetism. In this regard, the Neel-antiferromagnetism and the itinerant ferromagnetism are of central importance and great interest. Here we show that these magnetic orders can be achieved in the strongly interacting spin-1/2 trapped Fermi gases with additional p-wave interactions. In this strong coupling limit, the 1D trapped Fermi gas exhibit an effective Heisenberg spin XXZ chain in the anisotropic p-wave scattering channels. For a particular p-wave attraction or repulsion within the same species of fermionic atoms, the system displays ferromagnetic domains with full spin segregation or the anti-ferromagnetic spin configuration in the ground state. Such engineered magnetisms are likely to be probed in a quasi-1D trapped Fermi gas of $^{40}$ K atoms with very close s-wave and p-wave Feshbach resonances.

cond-mat.quant-gas↗

arXiv2015

Effective spin-chain model for strongly interacting one-dimensional atomic gases with an arbitrary spin

We present a general form of the effective spin-chain model for strongly interacting atomic gases with an arbitrary spin in the one-dimensional(1D) traps. In particular, for high-spin systems the atoms can collide in multiple scattering channels, and we find that the resulted form of spin-chain model generically follows the same structure as that of the interaction potentials. This is a unified form working for any spin, statistics (Bose or Fermi) and confinement potentials. We adopt the spin-chain model to reveal both the ferromagnetic(FM) and anti-ferromagnetic(AFM) magnetic orders for strongly interacting spin-1 bosons in 1D traps. We further show that by adding the spin-orbit coupling, the FM/AFM orders can be gradually destroyed and eventually the ground state exhibits universal spin structure and contacts that are independent of the strength of spin-orbit coupling.

cond-mat.quant-gas↗

arXiv2009

Many-body two-quantum coherences in semiconductor nanostructures

We present experimental coherent two-dimensional Fourier transform spectra of the exciton resonances in semiconductor quantum wells for a pulse sequence that isolates two-quantum coherences. By measuring the real part of the spectra, we can determine that the spectra are dominated by two quantum coherences due to many-body interactions, not bound biexcitons. Simulations performed using dynamics controlled truncation agree well with the experiments.

cond-mat.mes-hall↗

arXiv2007

Two-dimensional correlation spectroscopy of two-exciton resonances in semiconductor quantum wells

We propose a three-pulse coherent ultrafast optical technique that is particularly sensitive to two-exciton correlations. Two Liouville-space pathways for the density matrix contribute to this signal which reveals double quantum coherences when displayed as a two-dimensional correlation plot. Two-exciton couplings spread the cross peaks along both axes, creating a characteristic highly resolved pattern. This level of detail is not available from conventional one-dimensional four-wave mixing or other two-dimensional correlation spectroscopy signals such as the photo echo, in which two-exciton couplings show up along a single axis and are highly congested.

cond-mat.mes-hall↗

arXiv2007

A Coherent Nonlinear Optical Signal Induced by Electron Correlations

The correlated behavior of electrons determines the structure and optical properties of molecules, semiconductor and other systems. Valuable information on these correlations is provided by measuring the response to femtosecond laser pulses, which probe the very short time period during which the excited particles remain correlated. The interpretation of four-wave-mixing techniques, commonly used to study the energy levels and dynamics of many-electron systems, is complicated by many competing effects and overlapping resonances. Here we propose a coherent optical technique, specifically designed to provide a background-free probe for electronic correlations in many-electron systems. The proposed signal pulse is generated only when the electrons are correlated, which gives rise to an extraordinary sensitivity. The peak pattern in two-dimensional plots, obtained by displaying the signal vs. two frequencies conjugated to two pulse delays, provides a direct visualization and specific signatures of the many-electron wavefunctions.

cond-mat.mes-hall↗

arXiv2007

Two-Dimensional Optical Spectroscopy of Excitons in Semiconductor Quantum Wells: Liouville-space pathway analysis

We demonstrate how dynamic correlations of heavy-hole and light-hole excitons in semiconductor quantum wells may be investigated by two dimensional correlation spectroscopy (2DCS). The coherent response to three femtosecond optical pulses is predicted to yield cross (off-diagonal) peaks that contain direct signatures of many-body two-exciton correlations. Signals generated at various phase-matching directions are compared.

cond-mat.mes-hall↗