arXiv subjects

Tian Xiang

Publications and source records attributed to Tian Xiang.

At least 19 recordsLinked to original sources

arXiv2026

Quantum Metric Length as a Fundamental Length Scale in Disordered Flat Band Materials

Our previous understanding of electronic transport in disordered systems was based on the assumption that there is a finite Fermi velocity for the relevant electrons. The Fermi velocity determines important length scales in disordered systems such as the diffusion length and the localization length. However, in disordered systems with vanishing or nearly vanishing Fermi velocity, it is uncertain what determines the important length scales in such systems. In this work, we use the 1D Lieb lattice with isolated flat bands as an example to show that the quantum metric length (QML) is a fundamental length scale in the ballistic, diffusive and localization regimes. The QML is defined through the Bloch state wave functions of the flat bands. In the ballistic regime with short junctions, the QML controls the finite energy transport properties. In the localization regime with long junctions, the localization length is determined by the QML and remarkably, independent of disorder strength over a wide range of disorder strength. We call this unconventional localization regime, the quantum metric localization regime. In the diffusive regime, we demonstrate that the diffusion coefficient is linearly proportional to the QML via the wave-packet dynamics numerically. Importantly, the numerical results are consistent with the analytical results obtained through the Bethe-Salpeter equation. We conclude that the QML is a fundamentally important length scale governing the properties of disordered flat band materials.

cond-mat.mes-hall↗

arXiv2024

Disorder-induced diffusion transport in flat-band systems with quantum metric

Our previous understanding of transport in disordered system depends on the assumption that there is a well-defined Fermi velocity. The Fermi velocity determines important length scales in the system such as the diffusion length and localization length. However, nearly flat band materials with vanishing Fermi velocity, it is uncertain how to understand the disorder effects and what quantities determine the characteristic length scales in the system. In the clean limit, it is expected that the bulk transport is absent. In this work, we demonstrate, with a diamond lattice, that disorder can induce diffusion transport in a flat-band system with finite quantum metric. As disorder increases, the bulk transmission channels are activated, and the conductance reaches a maximum before decays inversely with disorder strength. Importantly, via the calculation of the wave-packet dynamics numerically, we show that the quantum metric determines the diffusion length of the system. Analytically, we show that the interplay between the disorder and quantum geometry gives rise to an effective Fermi velocity, as captured by the self-consistent Born approximation. The diffusion coefficient is identified from the Bethe-Salpeter equation under the ladder approximation. Our results reveal a disorder-driven delocalization mechanism in flat-band systems with finite quantum metric which cannot be understood by well-established theories of quantum diffusion. Our theory is important for understanding the disorder effects and transport properties of flat band materials such as twisted bilayer graphene which are current under intense investigation.

cond-mat.mes-hall↗

arXiv2024

Multi-Objective Trajectory Planning with Dual-Encoder

Time-jerk optimal trajectory planning is crucial in advancing robotic arms' performance in dynamic tasks. Traditional methods rely on solving complex nonlinear programming problems, bringing significant delays in generating optimized trajectories. In this paper, we propose a two-stage approach to accelerate time-jerk optimal trajectory planning. Firstly, we introduce a dual-encoder based transformer model to establish a good preliminary trajectory. This trajectory is subsequently refined through sequential quadratic programming to improve its optimality and robustness. Our approach outperforms the state-of-the-art by up to 79.72\% in reducing trajectory planning time. Compared with existing methods, our method shrinks the optimality gap with the objective function value decreasing by up to 29.9\%.

cs.RO↗

arXiv2023

Magnetic-order-mediated carrier and phonon dynamics in MnBi2Te4

We investigate the quasiparticle dynamics in MnBi2Te4 single crystal using the ultrafast optical spectroscopy. Our results show that there exist anomalous dynamical optical responses below the antiferromagnetic (AFM) ordering temperature TN. In specific, we reveal that both the initial carrier decay and recombination processes can be modulated via introducing the AFM order in sub-picosecond and picosecond timescales, respectively. We also discover a long relaxation process emerging below TN with a timescale approaching to the nanosecond regime, and can be attributed to the T-dependent spin-lattice interaction. There also emerges an unusual phonon energy renormalization below TN , which is found to arise from its coupling the spin degree via the exchange interaction and magnetic anisotropy. Our findings provide key information for understanding the dynamical properties of non-equilibrium carrier, spin and lattice in MnBi2Te4.

cond-mat.mtrl-sci↗

arXiv2023

Global solvability in a two-species chemotaxis system with signal production

In this work, we study the Neumann initial-boundary value problem for a two-species chemotaxis system with Lotka-Volterra competition and signal production. Under a rather weak and clean condition of sub-quadratic type damping and merely integrable initial data, we establish the global existence of generalized solutions in an N dimensional bounded and smooth domain.

math.AP↗

arXiv2022

On a cross-diffusive SIS epidemic model with power-like nonlinear incidence

In this work, we study global existence, boundedness and convergence of nonnegative classical solutions of a Neumann initial-boundary value problem for a cross diffusive SIS (susceptible-infected-susceptible) epidemic model with power-like infection mechanism generalizing the standard mass action mechanism. Global existence and boundedness of classical solutions are established in certain parameter ranges, and threshold/non-threshold long-time behaviors of global bounded solutions are also detected. Our findings significantly improve and extend previous related studies.

math.AP↗

arXiv2021

Global dynamics in a chemotaxis model describing tumor angiogenesis with/without mitosis in any dimensions

In this work, we study the Neumann initial boundary value problem for a three-component chemotaxis model in any dimensional bounded and smooth domains; this model is used to describe the branching of capillary sprouts during angiogenesis. First, we find three qualitatively simple sufficient conditions for qualitative global boundedness, and then, we establish two types of global stability for bounded solutions in qualitative ways. As a consequence of our findings, the underlying system without chemotaxis and the effect of ECs mitosis can not give rise to pattern formations. Our findings quantify and extend significantly previous studies, which are set in lower dimensional convex domains and are with no qualitative information.

math.AP↗

arXiv2021

Global solvability and asymptotical behavior in a two-species chemotaxis model with signal absorption

In this work, we study global existence, eventual smoothness and asymptotical behavior of positive solutions for a two-species chemotaxis consumption model in a bounded smooth but not necessarily convex domain $Ω\subset \mathbb{R}^n (n=2,3,4,5)$ with nonnegative initial data and homogeneous Neumann boundary data Under a smallness condition, boundedness of classical solutions and stabilization to constant equilibrium is known. Here, without any smallness condition, we show global existence and uniform-in-time boundedness of classical solutions in 2D and global existence, eventual smoothness and asymptotical behavior (in convex domains) of weak solutions in nD (n=3,4,5). Our findings also extend and improve the one-species chemotaxis-consumption model studied in relevant literature.

math.AP↗

arXiv2021

Dynamic DNN Decomposition for Lossless Synergistic Inference

Deep neural networks (DNNs) sustain high performance in today's data processing applications. DNN inference is resource-intensive thus is difficult to fit into a mobile device. An alternative is to offload the DNN inference to a cloud server. However, such an approach requires heavy raw data transmission between the mobile device and the cloud server, which is not suitable for mission-critical and privacy-sensitive applications such as autopilot. To solve this problem, recent advances unleash DNN services using the edge computing paradigm. The existing approaches split a DNN into two parts and deploy the two partitions to computation nodes at two edge computing tiers. Nonetheless, these methods overlook collaborative device-edge-cloud computation resources. Besides, previous algorithms demand the whole DNN re-partitioning to adapt to computation resource changes and network dynamics. Moreover, for resource-demanding convolutional layers, prior works do not give a parallel processing strategy without loss of accuracy at the edge side. To tackle these issues, we propose D3, a dynamic DNN decomposition system for synergistic inference without precision loss. The proposed system introduces a heuristic algorithm named horizontal partition algorithm to split a DNN into three parts. The algorithm can partially adjust the partitions at run time according to processing time and network conditions. At the edge side, a vertical separation module separates feature maps into tiles that can be independently run on different edge nodes in parallel. Extensive quantitative evaluation of five popular DNNs illustrates that D3 outperforms the state-of-the-art counterparts up to 3.4 times in end-to-end DNN inference time and reduces backbone network communication overhead up to 3.68 times.

cs.DC↗

arXiv2020

Negligibility of haptotaxis effect in a chemotaxis-haptotaxis model

In this work, we rigorously study chemotaxis effect versus haptotaxis effect on boundedness, blow-up and asymptotical behavior of solutions for a combined chemotaxis-haptotaxis model in 2D settings. It is well-known that the corresponding Keller-Segel chemotaxis-only model possesses a striking feature of critical mass blow-up phenomenon, namely, subcritical mass ensures boundedness, whereas, supercritical mass induces the existence of blow-ups. Herein, we show that this critical mass blow-up phenomenon stays almost the same in the full chemotaxis-haptotaxis model. For negligibility of haptotaxis on asymptotical behavior, we show that any global-in-time haptotaxis solution component vanishes exponentially as time approaches infinity, and the other two solution components converge exponentially to that of chemotaxis-only model in a global sense for suitably large chemo-sensitivity and in the usual sense for suitably small chemo-sensitivity. Therefore, the aforementioned critical mass blow-up phenomenon for the chemotaxis-only model is almost undestroyed even with arbitrary introduction of haptotaixs, showing negligibility of haptotaxis effect compared to chemotaxis effect in terms of boundedness, blow-up and longtime behavior in the chemotaxis-haptotaxis model.

math.AP↗

arXiv2020

On boundedness, gradient estimate, blow-up and convergence in a two-species and two-stimuli chemotaxis system with/without loop

In this work, we study dynamic properties of classical solutions to a homogenous Neumann initial-boundary value problem (IBVP) for a two-species and two-stimuli chemotaxis model with/without chemical signalling loop in a 2D bounded and smooth domain. We successfully detect the product of two species masses as a feature to determine boundedness, gradient estimates, blow-up and $W^{j,\infty}(1\leq j\leq 3)$-exponential convergence of classical solutions for the corresponding IBVP. More specifically, we first show generally a smallness on the product of both species masses, thus allowing one species mass to be suitably large, is sufficient to guarantee global boundedness, higher order gradient estimates and $W^{j,\infty}$-convergence with rates of convergence to constant equilibria; and then, in a special case, we detect a straight line of masses on which blow-up occurs for large product of masses. Our findings provide new understandings about the underlying model, and thus, improve and extend greatly the existing knowledge relevant to this model.

math.AP↗

arXiv2019

A new result for 2D boundedness of solutions to a chemotaxis--haptotaxis model with/without sub-logistic source

We consider the Neumann problem for a coupled chemotaxis-haptotaxis model of cancer invasion with/without kinetic source in a 2D bounded and smooth domain. For a large class of cell kinetic sources including zero source and sub-logistic sources, we detect an explicit condition involving the chemotactic strength, the asymptotic "damping" rate, and the initial mass of cells to ensure uniform-in-time boundedness for the corresponding Neumann problem. Our finding significantly improves existing 2D global existence and boundedness in related chemotaxis-/haptotaxis systems.

math.AP↗

arXiv2018

Dynamics and asymptotic profiles of endemic equilibrium for two frequency-dependent SIS epidemic models with cross-diffusion

This paper is concerned with two frequency-dependent SIS epidemic reaction-diffusion models in heterogeneous environment, with a cross-diffusion term modeling the effect that susceptible individuals tend to move away from higher concentration of infected individuals. It is first shown that the corresponding Neumann initial-boundary value problem in an $n$-dimensional bounded smooth domain possesses a unique global classical solution which is uniformly-in-time bounded regardless of the strength of the cross-diffusion and the spatial dimension $n$. It is further shown that, even in the presence of cross-diffusion, the models still admit threshold-type dynamics in terms of the basic reproduction number $\mathcal R_0$; that is, the unique disease free equilibrium is globally stable if $\mathcal R_0<1$, while if $\mathcal R_0>1$, the disease is uniformly persistent and there is an endemic equilibrium, which is globally stable in some special cases with weak chemotactic sensitivity. Our results on the asymptotic profiles of endemic equilibrium illustrate that restricting the motility of susceptible population may eliminate the infectious disease entirely for the first model with constant total population but fails for the second model with varying total population. In particular, this implies that such cross-diffusion does not contribute to the elimination of the infectious disease modelled by the second one.

math.AP↗

arXiv2018

Chemotaxis effect vs logistic damping on boundedness in the 2-D minimal Keller-Segel model

In this paper, we study chemotaxis effect vs logistic dampening on boundedness for the two-dimensional minimal Keller-Segel model with logistic source in a 2-D smooth and bounded domain. It is well-known that this model allows only for global and uniform-in-time bounded solutions for any chemotactic strength and logistic dampening. Here, we carefully employ a simple and new method to regain its boundedness and, with particular attention to how boundedness depends qualitatively on the coefficient of chemotactic strength and logistic dampening rate. Up to a scaling constant depending only on initial data and the domain, we provide explicit upper bounds for the the solution components of the corresponding initial-boundary value problem. This qualitative boundedness results seems to be the first result in the regard.

math.AP↗

arXiv2017

Sub-logistic source can prevent blow-up in the 2D minimal Keller-Segel chemotaxis system

It is well-known that the Neumann initial-boundary value problem for the minimal-chemotaxis-logistic system in a 2D bounded smooth domain has no blow-up for any choice of parameters. Here, for a large class of kinetic terms including sub-logistic sources, we show that the corresponding 2D Neumann initial-boundary value problems do not possess any blow-up. This illustrates a new phenomenon that even a class of sub-logistic sources can prevent blow-up for the 2D problem, indicating that logistic damping is not the weakest damping to guarantee uniform-in-time boundedness for the 2D minimal Keller-Segel chemotaxis model.

math.AP↗

arXiv2017

Convergence rates of solutions for a two-species chemotaxis-Navier-Stokes sytstem with competitive kinetics

In this paper, we study the rates of convergence of supposedly given global bounded classical solutions to a two-species chemotaxis-Navier-Stokes system with Lotka-Volterra competitive kinetics. Except in one case where the rate of convergence for the fluid component is expressed in terms of the Poincare constant and the model parameters, all other rates of convergence are shown to be expressible only in terms of the model parameters and the underlying space dimension.

math.AP↗

arXiv2016

How strong a logistic damping can prevent blow-up for the minimal Keller-Segel chemotaxis system?

In this paper, we study the minimal Keller-Segel model with a logistic source and obtain quantitative and qualitative descriptions of the competition between logistic damping and other ingredient, especially, chemotactic aggregation to guarantee boundedness and convergence. More specifically, we establish how precisely strong a logistic source can prevent blow-up, and then we obtain an explicit relationship between logistic damping and other ingredient, especially, chemotactic aggregation so that convergences are ensured and their respective convergence rates are explicitly calculated out. Known results in the literature are completed and refined. Furthermore, our findings provide clues on how to produce blowup solutions for KS chemotaxis models with logistic sources.

math.AP↗

arXiv2016

Boundedness and exponential convergence of a chemotaxis model for tumor invasion

We revisit the following chemotaxis system modeling tumor invasion \begin{equation*} \begin{cases} u_t=Δu-\nabla \cdot(u\nabla v),& x\inΩ, t>0,\\ v_t=Δv+wz,& x\inΩ, t>0,\\ w_t=-wz,& x\inΩ, t>0,\\ z_t=Δz-z+u, & x\inΩ, t>0,\\ \end{cases} \end{equation*} in a smooth bounded domain $Ω\subset \mathbb{R}^n(n\geq 1)$ with homogeneous Neumann boundary and initial conditions. This model was recently proposed by Fujie et al. \cite{FIY14} as a model for tumor invasion with the role of extracellular matrix incorporated, and was analyzed by Fujie et al. \cite{FIWY16}, showing the uniform boundedness and convergence for $n\leq 3$. In this work, we first show that the $L^\infty$-boundedness of the system can be reduced to the boundedness of $\|u(\cdot,t)\|_{L^{\frac{n}{4}+ε}(Ω)}$ for some $ε>0$ alone, and then, for $n\geq 4$, if the initial data $\|u_0\|_{L^{\frac{n}{4}}}$, $\|z_0\|_{L^\frac{n}{2}}$ and $\|\nabla v_0 \|_{L^n}$ are sufficiently small, we are able to establish the $L^\infty$-boundedness of the system. Furthermore, we show that boundedness implies exponential convergence with explicit convergence rate, which resolves the open problem left in \cite{FIWY16}.

math.AP↗