arXiv subjects

Qiao Liu

Publications and source records attributed to Qiao Liu.

69 records · Page 4Linked to original sources

arXiv2019

Learning Deep Multi-Level Similarity for Thermal Infrared Object Tracking

Existing deep Thermal InfraRed (TIR) trackers only use semantic features to describe the TIR object, which lack the sufficient discriminative capacity for handling distractors. This becomes worse when the feature extraction network is only trained on RGB images.To address this issue, we propose a multi-level similarity model under a Siamese framework for robust TIR object tracking. Specifically, we compute different pattern similarities on two convolutional layers using the proposed multi-level similarity network. One of them focuses on the global semantic similarity and the other computes the local structural similarity of the TIR object. These two similarities complement each other and hence enhance the discriminative capacity of the network for handling distractors. In addition, we design a simple while effective relative entropy based ensemble subnetwork to integrate the semantic and structural similarities. This subnetwork can adaptive learn the weights of the semantic and structural similarities at the training stage. To further enhance the discriminative capacity of the tracker, we construct the first large scale TIR video sequence dataset for training the proposed model. The proposed TIR dataset not only benefits the training for TIR tracking but also can be applied to numerous TIR vision tasks. Extensive experimental results on the VOT-TIR2015 and VOT-TIR2017 benchmarks demonstrate that the proposed algorithm performs favorably against the state-of-the-art methods.

cs.CV↗

arXiv2019

A reduction-to-absurdity approach using absolutely smooth solid surfaces to unveil the origins of wetting

Contact angle hysteresis and generation of dynamics angle are two fundamental phenomena about the contact angle deviation from the equilibrium state. Roughness on the solid surface, disjoining pressure in the thin film, and liquid-solid adhesion have all been considered as the origins of the phenomena. This work for the first time made a reduction to absurdity by employing absolutely smooth solid surfaces in ultra-large-scale molecular dynamic simulation. The results showed that the equilibrium angles were well established on the absolutely smooth surface just as regular, while the hysteresis and the dynamic angle vanished. The critical structure of the convex nanobending for advancing contact lines vanished as well. In contrast, the solids that made of atoms, even at the minimum roughness, would bring significant angle deviation and convex nanobending. A 3D observation was further made using state-of-the-art helium ion microscopy for the first time revealing the ubiquitous nanoscopic distortion along the contact line on atomically smooth surfaces. The results answer the question of the origin of the angle deviation, that the hysteresis and dynamic angle can be unified to originate from the friction, either static or dynamic; and at the same time resolve the puzzle of the hysteresis existence on reported smooth surfaces, showing that even the minimum i.e. atomic roughness is great enough to be effective on the contact line. The results are against the disjoining pressure theory which ignored the roughness and predicted the occurrence of the hysteresis on absolutely smooth solids.

cond-mat.soft↗

arXiv2018

Hierarchical Spatial-aware Siamese Network for Thermal Infrared Object Tracking

Most thermal infrared (TIR) tracking methods are discriminative, treating the tracking problem as a classification task. However, the objective of the classifier (label prediction) is not coupled to the objective of the tracker (location estimation). The classification task focuses on the between-class difference of the arbitrary objects, while the tracking task mainly deals with the within-class difference of the same objects. In this paper, we cast the TIR tracking problem as a similarity verification task, which is coupled well to the objective of the tracking task. We propose a TIR tracker via a Hierarchical Spatial-aware Siamese Convolutional Neural Network (CNN), named HSSNet. To obtain both spatial and semantic features of the TIR object, we design a Siamese CNN that coalesces the multiple hierarchical convolutional layers. Then, we propose a spatial-aware network to enhance the discriminative ability of the coalesced hierarchical feature. Subsequently, we train this network end to end on a large visible video detection dataset to learn the similarity between paired objects before we transfer the network into the TIR domain. Next, this pre-trained Siamese network is used to evaluate the similarity between the target template and target candidates. Finally, we locate the candidate that is most similar to the tracked target. Extensive experimental results on the benchmarks VOT-TIR 2015 and VOT-TIR 2016 show that our proposed method achieves favourable performance compared to the state-of-the-art methods.

cs.CV↗

arXiv2018

On optimal boundary control of Ericksen-Leslie system in dimension two

In this paper, we consider the boundary value problem of a simplified Ericksen-Leslie system in dimension two with non-slip boundary condition for the velocity field $u$ and time-dependent boundary condition for the director field $d$ of unit length. For such a system, we first establish the existence of a global weak solution that is smooth away from finitely many singular times, then establish the existence of a unique global strong solution that is smooth for $t>0$ under the assumption that the image of boundary data is contained in the hemisphere $\mathbb S^2_+$. Finally, we apply these theorems to the problem of optimal boundary control of the simplified Ericksen-Leslie system and show both the existence and a necessary condition of an optimal boundary control.

math.AP↗

arXiv2017

Global strong solution to the two-dimensional density-dependent nematic liquid crystal flows with vacuum

We are concerned with the Cauchy problem of the two-dimensional (2D) nonhomogeneous incompressible nematic liquid crystal flows on the whole space $\mathbb{R}^{2}$ with vacuum as far field density. It is proved that the 2D nonhomogeneous incompressible nematic liquid crystal flows admits a unique global strong solution provided the initial data density and the gradient of orientation decay not too slow at infinity, and the basic energy $\|\sqrt{ρ_0}\mathbf{u}_0\|_{L^2}^2+\|\nabla\mathbf{d}_0\|_{L^2}^2$ is small. In particular, the initial density may contain vacuum states and even have compact support. Moreover, the large time behavior of the solution is also obtained.

math.AP↗

arXiv2015

Gevrey analyticity of solutions to the 3D nematic liquid crystal flows in critical Besov space

We show that the solution to the Cauchy problem of the 3D nematic liquid crystal flows, with initial data belongs to a critical Besov space, belongs to a Gevrey class. More precisely, it is proved that for any $(u_{0},d_{0} - \overline{d}_{0}) \in \dot{B}^{\frac{3}{p}-1}_{p,1} (\mathbb{R}^{3}) \times \dot{B}^{\frac{3}{q}}_{q,1} (\mathbb{R}^{3})$ with some suitable conditions imposed on $p, q\in(1,\infty)$, there exists $T^{*}>0$ depending only on initial data, such that the nematic liquid crystal flows admits a unique solution $(u,d)$ on $\mathbb{R}^{3} \times (0,T^{*})$, and satisfies \begin{align*} \|e^{\sqrt{t} Λ_{1}}{u}(t) \|_{\widetilde{L}^{\infty}_{T^{*}} (\dot{B}^{\frac{3}{p}-1}_{p,1}) \cap \widetilde{L}^{1}_{T^{*}} (\dot{B}^{\frac{3}{p}+1}_{p,1})} + \|e^{\sqrt{t}Λ_{1}} ({d}(t)- \overline{d}_{0}) \|_{\widetilde{L}^{\infty}_{T^{*}} (\dot{B}^{\frac{3}{q}}_{q,1}) \cap \widetilde{L}^{1}_{T^{*}}(\dot{B}^{\frac{3}{q}+2}_{q,1})} < \infty. \end{align*} Here, $\overline{d}_{0} \in \mathbb{S}^{2}$ is a constant unit vector, and $Λ_{1}$ is the Fourier multiplier whose symbol is given by $|ξ|_{1}=|ξ_{1}|+|ξ_{2}|+|ξ_{3}|$. Moreover, if the initial data is sufficiently small enough, then $T^{*}=\infty$. As a consequence of the method, decay estimates of higher-order derivatives of solutions in Besov spaces are deduced.

math.AP↗

arXiv2015

Well-posedness and decay for the dissipative system modeling electro-hydrodynamics in negative Besov spaces

In \cite{GW12} (Y. Guo, Y. Wang, Decay of dissipative equations and negative Sobolev spaces, Commun. Partial Differ. Equ. 37 (2012) 2165--2208), Y. Guo and Y. Wang developed a general new energy method for proving the optimal time decay rates of the solutions to dissipative equations. In this paper, we generalize this method in the framework of homogeneous Besov spaces. Moreover, we apply this method to a model arising from electro-hydrodynamics, which is a coupled system of the Navier-Stokes equations and the Poisson-Nernst-Planck equations through charge transport and external forcing terms. We show that the negative Besov norms are preserved along time evolution, and obtain the optimal temporal decay rates of the higher-order spatial derivatives of solutions by the Fourier splitting approach and the interpolation techniques.

math.AP↗

arXiv2015

Global well-posedness of the 2D nonhomogeneous incompressible nematic liquid crystal flows with vacuum

This paper concerns the Cauchy problem of the two-dimensional (2D) nonhomogeneous incompressible nematic liquid crystal flows on the whole space $\mathbb{R}^{2}$ with vacuum as far field density. It is proved that the 2D nonhomogeneous incompressible nematic liquid crystal flows admits a unique global strong solution provided the initial data density and the gradient of orientation decay not too slow at infinity, and the initial orientation satisfies a geometric condition (see \eqref{eq1.3}). In particular, the initial data can be arbitrarily large and the initial density may contain vacuum states and even have compact support. As a byproduct, the large time behavior of the solution is also obtained.

math.AP↗

arXiv2014

On the temporal decay of solutions to the two-dimensional nematic liquid crystal flows

We consider the temporal decay estimates for weak solutions to the two-dimensional nematic liquid crystal flows, and we show that the energy norm of a global weak solution has non-uniform decay \begin{align*} \|u(t)\|_{L^{2}}+\|\nabla d(t)\|_{L^{2}}\rightarrow 0\quad \text{ as } t\rightarrow \infty, \end{align*} under suitable conditions on the initial data. We also show the exact rate of the decay (uniform decay) of the energy norm of the global weak solution.

math.AP↗

arXiv2013

Logarithmical Blow-up Criteria for the Nematic Liquid Crystal Flows

We investigate the blow-up criterion for the local in time classical solution of the nematic liquid crystal flows in dimension two and three. More precisely, $0<T_{*}<+\infty$ is the maximal time interval if and only if (i) for $n=3$, {align*} \int_{0}^{T_{*}}\frac{\|ω\|_{\dot{B}^{0}_{\infty,\infty}}+\|\nabla d\|_{\dot{B}^{0}_{\infty,\infty}}^{2}}{\sqrt{1+\text{ln}(e+\|ω\|_{\dot{B}^{0}_{\infty,\infty}} +\|\nabla d\|_{\dot{B}^{0}_{\infty,\infty}})}}\text{d}t=\infty, {align*} or {align*} \int_{0}^{T_{*}}\frac{\|\nabla u\|_{\dot{B}^{-1}_{\infty,\infty}}^{2}+\|\nabla d\|_{\dot{B}^{0}_{\infty,\infty}}^{2}}{\sqrt{1+\text{ln}(e+\|\nabla u\|_{\dot{B}^{-1}_{\infty,\infty}} +\|\nabla d\|_{\dot{B}^{0}_{\infty,\infty}})}}\text{d}t=\infty; {align*} and (ii) for $n=2$, {align*} \int_{0}^{T_{*}}\frac{\|\nabla d\|_{\dot{B}^{0}_{\infty,\infty}}^{2}}{\sqrt{1+\text{ln}(e +\|\nabla d\|_{\dot{B}^{0}_{\infty,\infty}})}}\text{d}t=\infty. {align*}

math.AP↗

arXiv2013

Logarithmically Improved Blow-up Criteria for a Phase Field Navier-Stokes Vesicle-Fluid Interaction Model

In this paper, we study a hydrodynamical system modeling the deformation of vesicle membrane under external incompressible viscous flow fields. The system is in the Eulerian formulation and is governed by the coupling of the incompressible Navier-Stokes equations with a phase field equation. In the three dimensional case, we establish two logarithmically improved blow-up criteria for local smooth solutions of this system in terms of the vorticity field only in the homogeneous Besov spaces.

math.AP↗

arXiv2012

A regularity criterion for the solution of the nematic liquid crystal flows in terms of $\dot{B}^{-1}_{\infty,\infty}$-norm

In this paper, we investigate regularity criterion for the solution of the nematic liquid crystal flows in dimension three and two. We prove the solution $(u,d)$ is smooth up to time $T$ provided that there exists a positive constant $\varepsilon_{0}>0$ such that (i) for n=3, |(u,\nabla d)|_{L^{\infty}(0,T;\dot{B}^{-1}_{\infty,\infty})}\leq \varepsilon_{0}, and (ii) for $n=2$, |\nabla d|_{L^{\infty}(0,T;\dot{B}^{-1}_{\infty,\infty})}\leq \varepsilon_{0}.

math.AP↗

arXiv2011

A Beale--Kato--Majda criterion for the 3-D Compressible Nematic Liquid Crystal Flows with Vacuum

In this paper, we prove a Beale--Kato--Majda blow-up criterion in terms of the gradient of the velocity only for the strong solution to the 3-D compressible nematic liquid crystal flows with nonnegative initial densities. More precisely, the strong solution exists globally if the $L^{1}(0,T;L^{\infty})$-norm of the gradient of the velocity $u$ is bounded. Our criterion improves the recent result of X. Liu and L. Liu (\cite{LL}, A blow-up criterion for the compressible liquid crystals system, arXiv:1011.4399v2 [math-ph] 23 Nov. 2010).

math.AP↗

arXiv2011

Existence of Solutions for the Debye-Hückel System with Low Regularity Initial Data

In this paper we study existence of solutions for the Cauchy problem of the Debye-Hückel system with low regularity initial data. By using the Chemin-Lerner time-space estimate for the heat equation, we prove that there exists a unique local solution if the initial data belongs to the Besov space $\dot{B}^{s}_{p,q}(\mathbb{R}^{n})$ for $-3/2<s\leq-2+\frac{n}{2}$, $p=\frac{n}{s+2}$ and $1\leq q\leq \infty$, and furthermore, if the initial data is sufficiently small then the solution is global. This result improves the regularity index of the initial data space in previous results on this model.

math.AP↗

arXiv2011

Global Existence and Stability for a Hydrodynamic System in the Nematic Liquid Crystal Flows

In this paper we consider a coupled hydrodynamical system which involves the Navier-Stokes equations for the velocity field and kinematic transport equations for the molecular orientation field. By applying the Chemin-Lerner's time-space estimates for the heat equation and the Fourier localization technique, we prove that when initial data belongs to the critical Besov spaces with negative-order, there exists a unique local solution, and this solution is global when initial data is small enough. As a corollary, we obtain existence of global self-similar solutions. In order to figure out the relation between the solution obtained here and weak solution of standard sense, we establish a stability result, which yields in a direct way that all global weak solutions associated with the same initial data must coincide with the solution obtained here, namely, weak-strong uniqueness holds.

math.AP↗