arXiv subjects

Xiaoxiao Zhang

Publications and source records attributed to Xiaoxiao Zhang.

9 recordsLinked to original sources

arXiv2025

Combinatorial Calabi flows with ideal circle patterns

In this paper, we extend the work of Ge-Hua-Zhou \cite{GHZ} on combinatorial Ricci flows for ideal circle patterns to combinatorial Calabi flows in both hyperbolic and Euclidean background geometry. We prove the solution to the combinatorial Calabi flows with any given initial Euclidean (hyperbolic resp.)ideal circle pattern exists for all time and converges exponentially fast to a flat cone metric (hyperbolic resp.) on a given surface.

math.DG↗

arXiv2023

Phases and magnetism at the microscale in compounds containing nominal Pb10-xCux(PO4)6O

Achieving superconductivity at room temperature could lead to substantial advancements in industry and technology. Recently, a compound known as Cu-doped lead-apatite, Pb10-xCux(PO4)6O (0.9 < x < 1.1), referred to as "LK-99", has been reported to exhibit unusual electrical and magnetic behaviors that appear to resemble a superconducting transition above room temperature. In this work we collected multiphase samples containing the nominal Pb10-xCux(PO4)6O phase (no superconductivity observed in our measured samples), synthesized by three independent groups, and studied their chemical, magnetic, and electrical properties at the microscale to overcome difficulties in bulk measurements. Through the utilization of optical, scanning electron, atomic force, and scanning diamond nitrogen-vacancy microscopy techniques, we are able to establish a link between local magnetic properties and specific microscale chemical phases. Our findings indicate that while the Pb10-xCux(PO4)6O phase seems to have a mixed magnetism contribution, a significant fraction of the diamagnetic response can be attributed to Cu-rich regions (e.g., Cu2S derived from a reagent used in the synthesis). Additionally, our electrical measurements reveal the phenomenon of current path switch and a change in resistance states of Cu2S. This provides a potential explanation for the electrical behavior observed in compounds related to Pb10-xCux(PO4)6O.

cond-mat.mtrl-sci↗

arXiv2021

A hierarchical residual network with compact triplet-center loss for sketch recognition

With the widespread use of touch-screen devices, it is more and more convenient for people to draw sketches on screen. This results in the demand for automatically understanding the sketches. Thus, the sketch recognition task becomes more significant than before. To accomplish this task, it is necessary to solve the critical issue of improving the distinction of the sketch features. To this end, we have made efforts in three aspects. First, a novel multi-scale residual block is designed. Compared with the conventional basic residual block, it can better perceive multi-scale information and reduce the number of parameters during training. Second, a hierarchical residual structure is built by stacking multi-scale residual blocks in a specific way. In contrast with the single-level residual structure, the learned features from this structure are more sufficient. Last but not least, the compact triplet-center loss is proposed specifically for the sketch recognition task. It can solve the problem that the triplet-center loss does not fully consider too large intra-class space and too small inter-class space in sketch field. By studying the above modules, a hierarchical residual network as a whole is proposed for sketch recognition and evaluated on Tu-Berlin benchmark thoroughly. The experimental results show that the proposed network outperforms most of baseline methods and it is excellent among non-sequential models at present.

cs.CV↗

arXiv2020

Transport of Finite Size Self-Propelled Particles Confined in a 2D Zigzag Channel with Gaussian Colored Noise

The directional transport of finite size self-propelled Brownian particles confined in a 2D zigzag channel with colored noise is investigated. The noises(noise parallel to x-axis and y-axis), the asymmetry parameter Δk, the ratio f(ratio of the particle radius and the bottleneck half width), the selfpropelled speed v0 have joint effect on the particles. The average velocity of self-propelled particles is significantly different from passive particles. The average velocity exhibits complicated behavior with increasing self-propelled speed v0

cond-mat.stat-mech↗

arXiv2019

Non-uniform Curvature and Anisotropic Deformation Control Wrinkling Patterns on Tori

We investigate wrinkling patterns in a tri-layer torus consisting of an expanding thin outer layer, an intermediate soft layer and an inner core with a tunable shear modulus, inspired by pattern formation in developmental biologies, such as follicle pattern formation during the development of chicken embryos. We show from large-scale finite element simulations that hexagonal wrinkling patterns form for stiff cores whereas stripe wrinkling patterns develop for soft cores. Hexagons and stripes co-exist to form hybrid patterns for cores with intermediate stiffness. The governing mechanism for the pattern transition is that the stiffness of the inner core controls the degree to which the major radius of the torus expands this has a greater effect on deformation in the long direction as compared to the short direction of the torus. This anisotropic deformation alters stress states in the outer layer which change from biaxial (preferred hexagons) to uniaxial (preferred stripes) compression as the core stiffness is reduced. As the outer layer continues to expand, stripe and hexagon patterns will evolve into Zigzag and segmented labyrinth, respectively. Stripe wrinkles are observed to initiate at the inner surface of the torus while hexagon wrinkles start from the outer surface as a result of curvature-dependent stresses in the torus. We further discuss the effects of elasticities and geometries of the torus on the wrinkling patterns.

cond-mat.soft↗

arXiv2018

Combinatorial $p$-th Calabi flows on surfaces

For triangulated surfaces and any $p>1$, we introduce the combinatorial $p$-th Calabi flow which precisely equals the combinatorial Calabi flows first introduced in H. Ge's thesis when $p=2$. The difficulties for the generalizations come from the nonlinearity of the $p$-th flow equation when $p\neq 2$. Adopting different approaches, we show that the solution to the combinatorial $p$-th Calabi flow exists for all time and converges if and only if there exists a circle packing metric of constant (zero resp.) curvature in Euclidean (hyperbolic resp.) background geometry. Our results generalize the work of H. Ge, Ge-Xu and Ge-Hua on the combinatorial Calabi flow from $p=2$ to any $p>1$.

math.DG↗

arXiv2018

The transport phenomenon of inertia Brownian particles in a periodic potential with non-Gaussian noise

The transport phenomenon (movement and diffusion) of inertia Brownian particles in a periodic potential with non-Gaussian noise is investigated. It is found that proper noise intensity Q will promote particles directional movement(or diffusion), but large Q will inhibit this phenomenon. For large value of Q, the average velocity V (or the diffusion coefficient D) has a maximum with increasing correlation time tau. But for small value of Q, V (or D) decreases with increasing tau. In some cases, for the same value of Q and the same value of tau, non-Gaussian noise can induce particles directional movement(or diffusion), but Gaussian colored noise can not.

cond-mat.stat-mech↗

arXiv2018

Positive Solutions of p-th Yamabe Type Equations on Infinite Graphs

Let $G=(V,E)$ be a connected infinite and locally finite weighted graph, $Δ_p$ be the $p$-th discrete graph Laplacian. In this paper, we consider the $p$-th Yamabe type equation $$-Δ_pu+h|u|^{p-2}u=gu^{α-1}$$ on $G$, where $h$ and $g$ are known, $2<α\leq p$. The prototype of this equation comes from the smooth Yamabe equation on an open manifold. We prove that the above equation has at least one positive solution on $G$.

math.AP↗

arXiv2017

Positive Solutions of $p$-th Yamabe Type Equations on Graphs

Let $G=(V,E)$ be a finite connected weighted graph, and assume $1\leqα\leq p\leq q$. In this paper, we consider the following $p$-th Yamabe type equation $$-Δ_pu+hu^{q-1}=λfu^{α-1}.$$ on $G$, where $Δ_p$ is the $p$-th discrete graph Laplacian, $h\leq0$ and $f>0$ are real functions defined on all vertices of $G$. Instead of the approach in [Ge3], we adopt a new approach, and prove that the above equation always has a positive solution $u>0$ for some constant $λ\in\mathbb{R}$. In particular, when $q=p$ our result generalizes the main theorem in [Ge3] from the case of $α\geq p>1$ to the case of $1\leqα\leq p$. It's interesting that our new approach can also work in the case of $α\geq p>1$.

math.DG↗