arXiv subjects

Bian Wu

Publications and source records attributed to Bian Wu.

14 recordsLinked to original sources

arXiv2026

Scalar anomalous dissipation and optimal regularity via iterated homogenization

For any $\beta_0<1/3$ we construct divergence free vector fields in $ C_{x,t}^{\beta_0}$ and a sequence of diffusivities $\kappa_q \searrow 0$ such that, for an arbitrary initial datum from a low regularity class, the classical solution $\rho_q$ to the advection-diffusion equation exhibits anomalous dissipation along the sequence $\kappa_q$. At the same time $\rho_q$ remains uniformly bounded in $C_t^{0} C_x^{\alpha_0}$, where $\beta_0 + 2\alpha_0<1$. Our result confirms a conjecture of Armstrong and Vicol \cite{ArmstrongVicol} and shows sharpness of the Obukhov-Corrsin threshold within the context of iterated homogenization. Our construction confirms time-homogeneity of the dissipation anomaly, as required in turbulence theory, and as a consequence we also obtain better time regularity for the scalar $\rho_q$ than the classical prediction of Yaglom.

math.AP↗

arXiv2025

MoEGCL: Mixture of Ego-Graphs Contrastive Representation Learning for Multi-View Clustering

In recent years, the advancement of Graph Neural Networks (GNNs) has significantly propelled progress in Multi-View Clustering (MVC). However, existing methods face the problem of coarse-grained graph fusion. Specifically, current approaches typically generate a separate graph structure for each view and then perform weighted fusion of graph structures at the view level, which is a relatively rough strategy. To address this limitation, we present a novel Mixture of Ego-Graphs Contrastive Representation Learning (MoEGCL). It mainly consists of two modules. In particular, we propose an innovative Mixture of Ego-Graphs Fusion (MoEGF), which constructs ego graphs and utilizes a Mixture-of-Experts network to implement fine-grained fusion of ego graphs at the sample level, rather than the conventional view-level fusion. Additionally, we present the Ego Graph Contrastive Learning (EGCL) module to align the fused representation with the view-specific representation. The EGCL module enhances the representation similarity of samples from the same cluster, not merely from the same sample, further boosting fine-grained graph representation. Extensive experiments demonstrate that MoEGCL achieves state-of-the-art results in deep multi-view clustering tasks. The source code is publicly available at https://github.com/HackerHyper/MoEGCL.

cs.CV↗

arXiv2024

Scale invariant bounds for the Kelvin-Helmholtz instability

We derive robust long-time a-priori estimates for the Navier-Stokes equation in a two-dimensional infinite strip which are uniform in the Reynolds number. These estimates provide several new scale invariant upper bounds for the size of the mixing layer in the Kelvin-Helmholtz instability.

math.AP↗

arXiv2024

Approximation of divergence-free vector fields vanishing on rough planar sets

Given any divergence-free vector field of Sobolev class $W^{m,p}_0(\Omega)$ in a bounded open subset $\Omega \subset \mathbb{R}^2$, we are interested in approximating it in the $W^{m,p}$ norm with divergence-free smooth vector fields compactly supported in $\Omega$. We show that this approximation property holds in the following cases: For $p>2$, this holds given that $\partial \Omega$ has zero Lebesgue measure (a weaker but more technical condition is sufficient); For $p \leq 2$, this holds if $\Omega^c$ can be decomposed into finitely many disjoint closed sets, each of which is connected or $d$-Ahlfors regular for some $d\in[0,2)$. This has links to the uniqueness of weak solutions to the Stokes equation in $\Omega$. For H\"older spaces, we prove this approximation property in general bounded domains.

math.AP↗

arXiv2024

Extremely asymmetric absorption and reflection near the exceptional point of three-dimensional metamaterial

In recent years, particular physical phenomena enabled by non-Hermitian metamaterial systems have attracted significant research interests. In this paper, a non-Hermitian three-dimensional metamaterial near the exceptional point (EP) is proposed to demonstrate extremely asymmetric absorption and reflection. Unlike its conventional counterparts, this proposed metamaterial is constructed with a loss-assisted design. Localized losses are introduced into the structure by combining our technique of graphene-based resistive inks with conventional printed circuit board (PCB) process. Extremely asymmetric absorption and reflection near the EP are experimentally observed by tuning the loss between split ring resonators (SRRs) in the meta-atoms. Simultaneously, by linking the equivalent circuit model (ECM) with the Hamiltonian quantum physical model, the equivalent non-Hermitian Hamiltonian is obtained and a non-Hermitian transmission matrix is constructed. We show that tuning the structure and circuit parameters of the ECM produces a metamaterial system with EP response. Our system can be used in the design of asymmetric metamaterial absorbers. Our work lays down the way for the manipulation of EP to develop perfect absorption, sensing and other applications in the 3D metamaterial platform.

physics.app-ph↗

arXiv2024

SignVTCL: Multi-Modal Continuous Sign Language Recognition Enhanced by Visual-Textual Contrastive Learning

Sign language recognition (SLR) plays a vital role in facilitating communication for the hearing-impaired community. SLR is a weakly supervised task where entire videos are annotated with glosses, making it challenging to identify the corresponding gloss within a video segment. Recent studies indicate that the main bottleneck in SLR is the insufficient training caused by the limited availability of large-scale datasets. To address this challenge, we present SignVTCL, a multi-modal continuous sign language recognition framework enhanced by visual-textual contrastive learning, which leverages the full potential of multi-modal data and the generalization ability of language model. SignVTCL integrates multi-modal data (video, keypoints, and optical flow) simultaneously to train a unified visual backbone, thereby yielding more robust visual representations. Furthermore, SignVTCL contains a visual-textual alignment approach incorporating gloss-level and sentence-level alignment to ensure precise correspondence between visual features and glosses at the level of individual glosses and sentence. Experimental results conducted on three datasets, Phoenix-2014, Phoenix-2014T, and CSL-Daily, demonstrate that SignVTCL achieves state-of-the-art results compared with previous methods.

cs.CV↗

arXiv2023

Anomalous dissipation and Euler flows

We show anomalous dissipation of scalars advected by weak solutions to the incompressible Euler equations with $C^{(\sfrac{1}{3})^-}$ regularity, for an arbitrary initial datum in $\dot H^1 (\T^3)$. This is the first rigorous derivation of zeroth law of scalar turbulence, where the scalar is advected by solution to an equation of hydrodynamics (unforced and deterministic). As a byproduct of our method, we provide a typicality statement for the drift, and recover certain desired properties of turbulence, including a lower bound on scalar variance commensurate with the Richardson pair dispersion hypothesis.

math.AP↗

arXiv2023

DPPMask: Masked Image Modeling with Determinantal Point Processes

Masked Image Modeling (MIM) has achieved impressive representative performance with the aim of reconstructing randomly masked images. Despite the empirical success, most previous works have neglected the important fact that it is unreasonable to force the model to reconstruct something beyond recovery, such as those masked objects. In this work, we show that uniformly random masking widely used in previous works unavoidably loses some key objects and changes original semantic information, resulting in a misalignment problem and hurting the representative learning eventually. To address this issue, we augment MIM with a new masking strategy namely the DPPMask by substituting the random process with Determinantal Point Process (DPPs) to reduce the semantic change of the image after masking. Our method is simple yet effective and requires no extra learnable parameters when implemented within various frameworks. In particular, we evaluate our method on two representative MIM frameworks, MAE and iBOT. We show that DPPMask surpassed random sampling under both lower and higher masking ratios, indicating that DPPMask makes the reconstruction task more reasonable. We further test our method on the background challenge and multi-class classification tasks, showing that our method is more robust at various tasks.

cs.CV↗

arXiv2023

Scale invariant bounds for mixing in the Rayleigh-Taylor instability

We study the Rayleigh-Taylor instability for two miscible, incompressible, inviscid fluids. Scale-invariant estimates for the size of the mixing zone and coarsening of internal structures in the fully nonlinear regime are established following techniques introduced for the Saffman-Taylor instability in [OttoMenon, 2004]. These bounds provide optimal scaling laws and reveal the strong role of dissipation in slowing down mixing.

math.AP↗

arXiv2022

On stable solutions to the Euler equations in convex planar domains

In convex planar domains, given an initial vorticity with one sign, we study the regularity and geometric properties of the dynamically stable solutions to the Euler equations in the coadjoint orbit of the initial vorticity. These flows have elliptic stagnation points. Under some nondegeneracy conditions on the data, we show they are Holder continuous and have convex level curves. We also give a detailed description for the set of stagnation points. If the initial vorticity has nice level set topology, these stable solutions are in the L^\infty-strong closure of the coadjoint orbit. We also demonstrate the sharpness of most assumptions we made.

math.AP↗

arXiv2021

Partially regular weak solutions of the stationary Navier-Stokes equations in dimension 6

By using defect measures, we prove the existence of partially regular weak solutions to the stationary Navier-Stokes equations with external force $f \in L_{\text{loc}}^q \cap L^{3/2}, q>3$ in general open subdomains of $\mathbb{R}^6$. These weak solutions satisfy certain local energy estimates and we estimate the size of their singular sets in terms of Hausdorff measures. We also prove the defect measures vanish under a smallness condition, in contrast to the nonstationary Navier-Stokes equations in $\mathbb{R}^4 \times [0,\infty[$.

math.AP↗

arXiv2021

On supercritical divergence-free drifts

For second-order elliptic or parabolic equations with subcritical or critical drifts, it is well-known that the Harnack inequality holds and their bounded weak solutions are Hölder continuous. We construct time-independent supercritical drifts in $L^{n-λ}(\mathbb{R}^n)$ with arbitrarily small $λ>0$ such that the Harnack inequality and the Hölder continuity fail in both the elliptic and the parabolic cases, thus confirming a conjecture by Seregin, Silvestre, Sverak and Zlatos. These results are sharp, and they also apply to a toy model of the axi-symmetric Navier-Stokes equations in space dimension $3$.

math.AP↗

arXiv2020

Partially regular weak solutions of the Navier-Stokes equations in $\mathbb{R}^4 \times [0,\infty[$

We show that for any given solenoidal initial data in $L^2$ and any solenoidal external force in $L_{\text{loc}}^q \bigcap L^{3/2}$ with $q>3$, there exist partially regular weak solutions of the Navier-Stokes equations in $\R^4 \times [0,\infty[$ which satisfy certain local energy inequalities and whose singular sets have locally finite $2$-dimensional parabolic Hausdorff measure. With the help of a parabolic concentration-compactness theorem we are able to overcome the possible lack of compactness arising in the spatially $4$-dimensional setting by using defect measures, which we then incorporate into the partial regularity theory.

math.AP↗

arXiv2019

A Low Profile Tunable Microwave Absorber based on Graphene Sandwich Structure and High Impedance Surface

In this paper, a low profile dynamically tunable microwave absorber is proposed, which consists of high impedance surface (HIS) and graphene sandwich structure (GSS). We theoretically demonstrate and experimentally verify that the proposed absorber can provide a dynamically tunable reflection range from larger than -3dB to less than -30 dB (corresponding to the absorption range from 50% to 99.9%) at opera-ting frequency of 11.2GHz by external bias voltage. The entire thickness of this absorber is only 2.8mm, nearly one tenth of working wavelength. In addition, a modified equivalent circuit model is proposed to explicate its absorption mechanism. At last, we fabricate a prototype absorber, and measure its absorption in anechoic chamber. The experimental results agree well with the full wave simulation results. This work may provide a reference for design and fabrication of dynamically tunable microwave absorber based on large-scale graphene and may promote the actual applications of graphene at microwave frequency.

physics.app-ph↗