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Yong Lu

Publications and source records attributed to Yong Lu.

At least 73 records · Page 4Linked to original sources
arXiv2020

Homogenization of Poisson and Stokes equations in the whole space

We consider the homogenization of the Poisson and the Stokes equations in the whole space perforated with periodically distributed small holes. The periodic homogenization in bounded domains is well understood, following the classical results in [24, 4, 1, 2]. In this paper, we show that these classical homogenization results in a bounded domain can be extended to the whole space ${\mathbb R}^d$. Our results cover all three cases corresponding to different sizes of holes and cover all $d\geq 2$.

math.AP↗
arXiv2020

Homogenization of stationary Navier--Stokes--Fourier system in domains with tiny holes

We study the homogenization of stationary compressible Navier--Stokes--Fourier system in a bounded three dimensional domain perforated with a large number of very tiny holes. Under suitable assumptions imposed on the smallness and distribution of the holes, we show that the homogenized limit system remains the same in the domain without holes.

math.AP↗
arXiv2019

Characterizing decoherence rates of a superconducting qubit by direct microwave scattering

We experimentally investigate a superconducting qubit coupled to the end of an open transmission line, in a regime where the qubit decay rates to the transmission line and to its own environment are comparable. We perform measurements of coherent and incoherent scattering, on- and off-resonant fluorescence, and time-resolved dynamics to determine the decay and decoherence rates of the qubit. In particular, these measurements let us discriminate between non-radiative decay and pure dephasing. We combine and contrast results across all methods and find consistent values for the extracted rates. The results show that the pure dephasing rate is one order of magnitude smaller than the non-radiative decay rate for our qubit. Our results indicate a pathway to benchmark decoherence rates of superconducting qubits in a resonator-free setting.

quant-ph↗
arXiv2019

Homogenization of Stokes equations in perforated domains: a unified approach

We consider the homogenization of the Stokes equations in a domain perforated with a large number of small holes which are periodically distributed. In [1,2], Allaire gave a systematic study on this problem. In this paper, we introduce a unified proof for different sizes of holes for the homogenization of the Stokes equations by employing a generalized cell problem inspired by Tartar [17].

math.AP↗
arXiv2019

Global existence of large data weak solutions for a simplified compressible Oldroyd--B model without stress diffusion

We start with the compressible Oldroyd--B model derived in \cite{Barrett-Lu-Suli} ({\em J. W. Barrett, Y. Lu, E. Süli. Existence of large-data finite-energy global weak solutions to a compressible Oldroyd--B model. Comm. Math. Sci. 15 (2017), 1265--1323}), where the existence of global-in-time finite-energy weak solutions was shown in two dimensional setting with stress diffusion. In the paper, we investigate the case without stress diffusion. We first restrict ourselves to the corotational setting as in \cite{LM00} ({\em P. L. Lions, N. Masmoudi. Global solutions for some Oldroyd models of non-Newtonian flows. Chin. Ann. Math., Ser. B 21(2) (2000), 131--146.}) We further assume the extra stress tensor is a scalar matrix and we derive a simplified model which takes a similar form as the multi-component compressible Navier--Stokes equations, where, however, the pressure term related to the scalar extra stress tensor has the opposite sign. By employing the techniques developed in \cite{VWY19, Novotny-Pokorny-19}, we can still prove the global-in-time existence of finite energy weak solutions in two or three dimensions, without the presence of stress diffusion.

math.AP↗
arXiv2019

Numerical study of Wigner negativity in one-dimensional steady-state resonance fluorescence

In a numerical study, we investigate the steady-state generation of nonclassical states of light from a coherently driven two-level atom in a one-dimensional waveguide. Specifically, we look for states with a negative Wigner function, since such nonclassical states are a resource for quantum information processing applications, including quantum computing. We find that a waveguide terminated by a mirror at the position of the atom can provide Wigner-negative states, while an infinite waveguide yields strictly positive Wigner functions. Moreover, our investigation reveals a connection between the purity of a quantum state and its Wigner negativity. We also analyze the effects of decoherence on the negativity of a state.

quant-ph↗
arXiv2019

Surrogate Supervision for Medical Image Analysis: Effective Deep Learning From Limited Quantities of Labeled Data

We investigate the effectiveness of a simple solution to the common problem of deep learning in medical image analysis with limited quantities of labeled training data. The underlying idea is to assign artificial labels to abundantly available unlabeled medical images and, through a process known as surrogate supervision, pre-train a deep neural network model for the target medical image analysis task lacking sufficient labeled training data. In particular, we employ 3 surrogate supervision schemes, namely rotation, reconstruction, and colorization, in 4 different medical imaging applications representing classification and segmentation for both 2D and 3D medical images. 3 key findings emerge from our research: 1) pre-training with surrogate supervision is effective for small training sets; 2) deep models trained from initial weights pre-trained through surrogate supervision outperform the same models when trained from scratch, suggesting that pre-training with surrogate supervision should be considered prior to training any deep 3D models; 3) pre-training models in the medical domain with surrogate supervision is more effective than transfer learning from an unrelated domain (e.g., natural images), indicating the practical value of abundant unlabeled medical image data.

cs.CV↗
arXiv2018

Uniform estimates for Stokes equations in a domain with a small hole and applications in homogenization problems

We consider the Dirichlet problem of the Stokes equations in a domain with a shrinking hole in $\mathbb{R}^d, \ d\geq 2$. A typical observation is that, the Lipschitz norm of the domain goes to infinity as the size of the hole goes to zero. Thus, if $p\neq 2$, the classical results indicate that the $W^{1,p}$ estimate of the solution may go to infinity as the size of the hole tends to zero. In this paper, we give a complete description for the uniform $W^{1,p}$ estimates of the solution for all $1<p<\infty$. We show that the uniform $W^{1,p}$ estimate holds if and only if $d'<p<d$ ($p=2$ when $d=2$). We then give two applications in the study of homogenization problems in fluid mechanics: a generalization of the restriction operator and a construction of Bogovskii type operator in perforated domains with a quantitative estimate of the operator norm.

math.AP↗
arXiv2018

Homogenization of a non-homogeneous fluid

We consider a non--homogeneous incompressible and heat conducting fluid confined to a 3D domain perforated by tiny holes. The ratio of the diameter of the holes and their mutual distance is critical, the former being equal to $ε^3$, the latter proportional to $ε$, where $ε$ is a small parameter. We identify the asymptotic limit for $ε\to 0$, in which the momentum equation contains a friction term of Brinkman type determined uniquely by the viscosity and geometric properties of the perforation. Besides the inhomogeneity of the fluid, we allow the viscosity and the heat conductivity coefficient to depend on the temperature, where the latter is determined via the Fourier law with homogenized (oscillatory) heat conductivity coefficient that is different for the fluid and the solid holes. To the best of our knowledge, this is the first result in the critical case for the inhomogenous heat--conducting fluid.

math.AP↗
arXiv2017

The rank of a complex unit gain graph in terms of the rank of its underlying graph

Let $Φ=(G, φ)$ be a complex unit gain graph (or $\mathbb{T}$-gain graph) and $A(Φ)$ be its adjacency matrix, where $G$ is called the underlying graph of $Φ$. The rank of $Φ$, denoted by $r(Φ)$, is the rank of $A(Φ)$. Denote by $θ(G)=|E(G)|-|V(G)|+ω(G)$ the dimension of cycle spaces of $G$, where $|E(G)|$, $|V(G)|$ and $ω(G)$ are the number of edges, the number of vertices and the number of connected components of $G$, respectively. In this paper, we investigate bounds for $r(Φ)$ in terms of $r(G)$, that is, $r(G)-2θ(G)\leq r(Φ)\leq r(G)+2θ(G)$, where $r(G)$ is the rank of $G$. As an application, we also prove that $1-θ(G)\leq\frac{r(Φ)}{r(G)}\leq1+θ(G)$. All corresponding extremal graphs are characterized.

math.CO↗
arXiv2017

Relative entropy, weak-strong uniqueness and conditional regularity for a compressible Oldroyd-B model

We consider the compressible Oldroyd-B model derived in \cite{Barrett-Lu-Suli}, where the existence of global-in-time finite energy weak solutions was shown in two dimensional setting. In this paper, we first state a local well-posedness result for this compressible Oldroyd-B model. In two dimensional setting, we give a (refined) blow-up criterion involving only the upper bound of the fluid density. We then show that, if the initial fluid density and polymer number density admit a positive lower bound, the weak solution coincides with the strong one as long as the latter exists. Moreover, if the fluid density of a weak solution issued from regular initial data admits a finite upper bound, this weak solution is indeed a strong one; this can be seen as a corollary of the refined blow-up criterion and the weak-strong uniqueness.

math.AP↗
arXiv2017

Homogenization of the compressible Navier-Stokes equations in domains with very tiny holes

We consider the homogenization problem of the compressible Navier-Stokes equations in a bounded three dimensional domain perforated with very tiny holes. As the number of holes increases to infinity, we show that, if the size of the holes is small enough, the homogenized equations are the same as the compressible Navier-Stokes equations in the homogeneous domain---domain without holes. This coincides with the previous studies for the Stokes equations and the stationary Navier-Stokes equations. It is the first result of this kind in the instationary barotropic compressible setting. The main technical novelty is the study of the Bogovskii operator in non-Lipschitz domains.

math.AP↗
arXiv2017

Qualitative Action Recognition by Wireless Radio Signals in Human-Machine Systems

Human-machine systems required a deep understanding of human behaviors. Most existing research on action recognition has focused on discriminating between different actions, however, the quality of executing an action has received little attention thus far. In this paper, we study the quality assessment of driving behaviors and present WiQ, a system to assess the quality of actions based on radio signals. This system includes three key components, a deep neural network based learning engine to extract the quality information from the changes of signal strength, a gradient based method to detect the signal boundary for an individual action, and an activitybased fusion policy to improve the recognition performance in a noisy environment. By using the quality information, WiQ can differentiate a triple body status with an accuracy of 97%, while for identification among 15 drivers, the average accuracy is 88%. Our results show that, via dedicated analysis of radio signals, a fine-grained action characterization can be achieved, which can facilitate a large variety of applications, such as smart driving assistants.

cs.HC↗
arXiv2016

Skew-rank of an oriented graph in terms of the rank and dimension of cycle space of its underlying graph

Let $G^σ$ be an oriented graph and $S(G^σ)$ be its skew-adjacency matrix, where $G$ is called the underlying graph of $G^σ$. The skew-rank of $G^σ$, denoted by $sr(G^σ)$, is the rank of $S(G^σ)$. Denote by $d(G)=|E(G)|-|V(G)|+θ(G)$ the dimension of cycle spaces of $G$, where $|E(G)|$, $|V(G)|$ and $θ(G)$ are the edge number, vertex number and the number of connected components of $G$, respectively. Recently, Wong, Ma and Tian [European J. Combin. 54 (2016) 76--86] proved that $sr(G^σ)\leq r(G)+2d(G)$ for an oriented graph $G^σ$, where $r(G)$ is the rank of the adjacency matrix of $G$, and characterized the graphs whose skew-rank attain the upper bound. However, the problem of the lower bound of $sr(G^σ)$ of an oriented graph $G^σ$ in terms of $r(G)$ and $d(G)$ of its underlying graph $G$ is left open till now. In this paper, we prove that $sr(G^σ)\geq r(G)-2d(G)$ for an oriented graph $G^σ$ and characterize the graphs whose skew-rank attain the lower bound.

math.CO↗
arXiv2016

Hermitian-Randić matrix and Hermitian-Randić energy of mixed graphs

Let $M$ be a mixed graph and $H(M)$ be its Hermitian-adjacency matrix. If we add every edge and arc in $M$ a Randić weight, then we can get a new weighted Hermitian-adjacency matrix. What are the properties of this new matrix? Motivated by this, we define the Hermitian-Randić matrix $R_{H}(M)=(r_{h})_{kl}$ of a mixed graph $M$, where $(r_{h})_{kl}=-(r_{h})_{lk}=\frac{\textbf{i}}{\sqrt{d_{k}d_{l}}}$ ($\textbf{i}=\sqrt{-1}$) if $(v_{k},v_{l})$ is an arc of $M$, $(r_{h})_{kl}=(r_{h})_{lk}=\frac{1}{\sqrt{d_{k}d_{l}}}$ if $v_{k}v_{l}$ is an undirected edge of $M$, and $(r_{h})_{kl}=0$ otherwise. In this paper, firstly, we compute the characteristic polynomial of the Hermitian-Randić matrix of a mixed graph. Furthermore, we give bounds to the Hermitian-Randić energy of a general mixed graph. Finally, we give some results about the Hermitian-Randić energy of mixed trees.

math.CO↗
arXiv2016

Existence of large-data finite-energy global weak solutions to a compressible Oldroyd-B model

A compressible Oldroyd--B type model with stress diffusion is derived from a compressible Navier--Stokes--Fokker--Planck system arising in the kinetic theory of dilute polymeric fluids, where polymer chains immersed in a barotropic, compressible, isothermal, viscous Newtonian solvent, are idealized as pairs of massless beads connected with Hookean springs. We develop a-priori bounds for the model, including a logarithmic bound, which guarantee the nonnegativity of the elastic extra stress tensor, and we prove the existence of large data global-in-time finite-energy weak solutions in two space dimensions.

math.AP↗