Searcharxiv⌕ Search

arXiv subjects

Xiaomin Zhang

Publications and source records attributed to Xiaomin Zhang.

At least 19 recordsLinked to original sources
arXiv2026

Shock solutions of a 3D spherical piston problem for the compressible Euler equations

This paper establishes the global well-posedness of shock solutions for a 3D spherical piston problem to the compressible Euler equations. The main mathematical challenges are the nonlinear coupling between the free shock boundary and the moving piston, alongside potential gradient catastrophes induced by spherical geometric source terms. To overcome these difficulties, we reformulate the problem using Riemann invariants and introduce a tailored directional derivative along the unperturbed piston trajectory. Then we can extend the local solution to construct a global piecewise smooth solution including a single shock under some moderate assumptions.

math.AP↗
arXiv2026

Perturbation Analysis of Gravitational Collapse of Gaseous Stars in the Pressureless Euler-Poisson System

The compressible Euler-Poisson system describes the full evolutionary processes of inviscid compressible gases, including compression, expansion, fluid motion, equilibrium states and gravitational collapse, under the combined effects of self-gravitation, pressure and inertial forces. It constitutes the fundamental macroscopic mathematical model for describing stellar structures, nebular evolution and gravitational collapse of gaseous celestial bodies. The system comprises mass conservation, momentum conservation, energy conservation laws coupled with the Poisson equation. Following the research in \cite{huang2022}, this paper investigates the quantitative relations among the relative perturbation amplitude of initial velocity, critical time and collapse time for gaseous stars undergoing gravitational collapse within the framework of the pressureless Euler-Poisson system. The closed-form formulas are verified against direct numerical integration, the accuracy of the asymptotic power law is quantified, and the relation between the two time scales is examined.

math.AP↗
arXiv2026

FTD-GNO: Memory-Efficient Graph Neural Operators through Functional Tensor Decomposition of the Kernel

Graph Neural Operators (GNOs) provide flexible surrogate models for learning solution operators of partial differential equations (PDEs). However, standard GNOs typically parameterize the integral kernel with a monolithic neural network and evaluate kernel interactions over graph edges, leading to substantial computational and memory overhead at high resolutions or with large neighborhoods. To address these limitations, we propose Functional Tensor Decomposition Graph Neural Operator (FTD-GNO), a memory-efficient GNO framework that decouples the high-dimensional continuous integral kernel into low-dimensional mode-wise functions. By instantiating the kernel with classical tensor decomposition formats, including CP, Tensor-Train, and Tucker decompositions, FTD-GNO enables algebraic reconstruction of the integral operator without explicitly materializing full edge-wise kernel tensors. This factorized formulation reduces the memory footprint of kernel evaluation and aggregation while retaining the continuous operator-learning structure of GNOs. Theoretical complexity analysis shows that FTD-GNO substantially lowers parameter and activation-memory costs associated with high-dimensional kernel construction. Experiments show lower peak memory than the corresponding unfactorized graph-integral baselines, with shorter recorded training times. Fourier-graph experiments further demonstrate that FTD can improve the efficiency of a graph-integral layer within a hybrid operator and has good scalability.

cs.LG↗
arXiv2026

On the Well-Posedness of Periodic Strong Transonic Shocks in Divergent Nozzles

This paper studies the $C^1$ existence and dynamical stability of temporal periodic solutions involving strong transonic shocks for the quasi--one--dimensional full compressible Euler equations in diverging nozzles. We reveal the physical structural dissipation mechanism of strong transonic shocks hidden in the Rankine--Hugoniot conditions. This allows us to estimate the resonance at the shock boundary caused by the left acoustic waves in the subsonic downstream region. With this dissipation, we complete the proof by developing a fraction--step linearized iterative method.

math.AP↗
arXiv2026

Existence of detonation wave solutions to the piston problem for the Zeldovich-von Neumann-D{ö}ring combustion model

In this paper, we study detonation wave solutions to one-dimensional piston problem for the Zeldovich-von Neumann-D{ö}ring (ZND) combustion model with a one-step exothermic chemical reaction. As a special type of shock wave, the position of the detonation wave is unknown, which make our model to be a free boundary problem.~The global existence of detonation wave solutions to this free boundary problem is proved. Compared with previous result~\cite{Lai}, we do not impose any dissipation conditions on the equations and the boundaries.

math.AP↗
arXiv2025

SateLight: A Satellite Application Update Framework for Satellite Computing

Satellite computing is an emerging paradigm that empowers satellites to perform onboard processing tasks (i.e., \textit{satellite applications}), thereby reducing reliance on ground-based systems and improving responsiveness. However, enabling application software updates in this context remains a fundamental challenge due to application heterogeneity, limited ground-to-satellite bandwidth, and harsh space conditions. Existing software update approaches, designed primarily for terrestrial systems, fail to address these constraints, as they assume abundant computational capacity and stable connectivity. To address this gap, we propose SateLight, a practical and effective satellite application update framework tailored for satellite computing. SateLight leverages containerization to encapsulate heterogeneous applications, enabling efficient deployment and maintenance. SateLight further integrates three capabilities: (1) a content-aware differential strategy that minimizes communication data volume, (2) a fine-grained onboard update design that reconstructs target applications, and (3) a layer-based fault-tolerant recovery mechanism to ensure reliability under failure-prone space conditions. Experimental results on a satellite simulation environment with 10 representative satellite applications demonstrate that SateLight reduces transmission latency by up to 91.18% (average 56.54%) compared to the best currently available baseline. It also consistently ensures 100% update correctness across all evaluated applications. Furthermore, a case study on a real-world in-orbit satellite demonstrates the practicality of our approach.

cs.SE↗
arXiv2025

Anomalous magnetoresistance in an antiferromagnetic Kagome semimetal heterostructures

Antiferromagnetic Kagome semimetals have attracted tremendous attentions for their potential application in antiferromagnetic topological spintronics. Effectively manipulating Kagome antiferromagnetic states could reveal abundant physical phenomena induced from quantum interactions between topology, spin, and correlation. Here, we achieved tunable spin textures of FeSn thin films via introducing interfacial Dzyaloshinskii Moriya interaction from heavy-metal Pt overlayer. With increasing FeSn thickness, the variable spin textures result in gradual change in Hall resistivity and magnetoresistance. Importantly, an unconventional damped oscillatory-like behavior of magnetoresistance at relatively low magnetic field can be observed in thin FeSn-Pt samples. This oscillatory like magnetoresistance feature was confirmed to be related to the special topological spin textures revealed by magnetic force microscopy measurements. The formation of rich variety of topological spin textures in association with exotic magneto-transport properties in antiferromagnetic Kagome FeSn heterostructures offers new perspectives for understanding the novel emergent phenomena in Kagome antiferromagnets.

cond-mat.mtrl-sci↗
arXiv2025

Time-periodic transonic shock solution in divergent nozzles

We demonstrate that it is possible to control a normal transonic shock to move periodically by adjusting the boundary conditions at the entrance or the exit of the tube, for which, the phenomena has been observed in engineering. In this paper, we describe the gas by a quasi-one-dimensional compressible Euler equations with temporal periodic boundary conditions and prove the global existence and dynamical stability of the time-periodic transonic shock solution with an iteration method. The major difficulty is to determine the position of the moving shock front, which can be obtained by a free boundary problem in the subsonic domain. We decouple this free boundary problem by the $Rankine-Hugoniot$ conditions and a two-step iteration process.

math.AP↗
arXiv2025

Unconventional bias-dependent tunneling magnetoresistance in van der Waals ferromagnetic/semiconductor heterojunctions

Two-dimensional van der Waals (vdW) ferromagnetic/semiconductor heterojunctions represent an ideal platform for studying and exploiting tunneling magnetoresistance (TMR) effects due to the versatile band structure of semiconductors and their high-quality interfaces. In the all-vdW magnetic tunnel junction (MTJ) devices, both the magnitude and sign of the TMR can be tuned by an applied voltage. Typically, as the bias voltage increases, first the amplitude of the TMR decreases, then the sign of the TMR reverses and/or oscillates. Here, we report on an unconventional bias-dependent TMR in the all-vdW Fe3GaTe2/GaSe/Fe3GaTe2 MTJs, where the TMR first increases, then decreases, and finally undergoes a sign reversal as the bias voltage increases. This dependence cannot be explained by traditional models of MTJs. We propose an in-plane electron momentum (k//) resolved tunneling model that considers both the coherent degree of k// and the decay of the electron wave function through the semiconductor spacer layer. This can explain well the conventional and unconventional bias-dependent TMR. Our results thus provide a deeper understanding of the bias-dependent spin-transport in semiconductor-based MTJs and offer new insights into semiconductor spintronics.

cond-mat.mtrl-sci↗
arXiv2023

Subsonic time-periodic solution to damped compressible Euler equations with large entropy

In this paper, one-dimensional nonisentropic compressible Euler equations with linear damping $α(x)ρu$ are analyzed.~We want to explore the conditions under which a subsonic temporal periodic boundary can trigger a time-periodic $C^{1}$ solution. To achieve this aim, we use a technically constructed iteration scheme and give the sufficient conditions to guarantee the existence, uniqueness and stability of the $C^{1}$ time-periodic solutions on the perturbation of a subsonic Fanno flow.~It is worthy to be pointed out that the entropy exhibits large amplitude under the assumption that the inflow sound speed is small.~However, it is crucial to assume that the boundary conditions possess a kind of dissipative structure at least on one side, which is used to cancel the nonlinear accelerating effect in the system.~The results indicate that the time-periodic feedback boundary control with dissipation can stabilize the nonisentropic compressible Euler equations around the Fanno flows.

math.AP↗
arXiv2023

Room-temperature van der Waals 2D ferromagnet switching by spin-orbit torques

Emerging wide varieties of the two-dimensional (2D) van der Waals (vdW) magnets with atomically thin and smooth interfaces holds great promise for next-generation spintronic devices. However, due to the lower Curie temperature of the vdW 2D ferromagnets than room temperature, electrically manipulating its magnetization at room temperature has not been realized. In this work, we demonstrate the perpendicular magnetization of 2D vdW ferromagnet Fe3GaTe2 can be effectively switched at room temperature in Fe3GaTe2/Pt bilayer by spin-orbit torques (SOTs) with a relatively low current density of 1.3 10^7A/cm2. Moreover, the high SOT efficiency of ξ_{DL}~0.22 is quantitatively determined by harmonic measurements, which is higher than those in Pt-based heavy metal/conventional ferromagnet devices. Our findings of room-temperature vdW 2D ferromagnet switching by SOTs provide a significant basis for the development of vdW-ferromagnet-based spintronic applications.

physics.app-ph↗
arXiv2023

Tightening Discretization-based MILP Models for the Pooling Problem using Upper Bounds on Bilinear Terms

Discretization-based methods have been proposed for solving nonconvex optimization problems with bilinear terms such as the pooling problem. These methods convert the original nonconvex optimization problems into mixed-integer linear programs (MILPs). In this paper we study tightening methods for these MILP models for the pooling problem, and derive valid constraints using upper bounds on bilinear terms. Computational results demonstrate the effectiveness of our methods in terms of reducing solution time.

math.OC↗
arXiv2022

Subsonic time-periodic solution to compressible Euler equations with damping in a bounded domain

In this paper, we consider the one-dimensional isentropic compressible Euler equations with linear damping $β(t,x)ρu$ in a bounded domain, which can be used to describe the process of compressible flows through a porous medium.~And the model is imposed a dissipative subsonic time-periodic boundary condition.~Our main results reveal that the time-periodic boundary can trigger a unique subsonic time-periodic smooth solution which is stable under small perturbations on initial data. Moreover, the time-periodic solution possesses higher regularity and stability provided a higher regular boundary condition.

math.AP↗
arXiv2022

Global existence and stability of subsonic time-periodic solution to the damped compressible Euler equations in a bounded domain

In this paper, we consider the one-dimensional isentropic compressible Euler equations with source term $β(t,x)ρ|u|^αu$ in a bounded domain, which can be used to describe gas transmission in a nozzle.~The model is imposed a subsonic time-periodic boundary condition.~Our main results reveal that the time-periodic boundary can trigger an unique subsonic time-periodic smooth solution and this unique periodic solution is stable under small perturbations on initial and boundary data.~To get the existence of subsonic time-periodic solution, we use the linear iterative skill and transfer the boundary value problem into two initial value ones by using the hyperbolic property of the system. Then the corresponding linearized system can be decoupled.~The uniqueness is a direct by-product of the stability. There is no small assumptions on the damping coefficient.

math.AP↗
arXiv2022

On the identifiability of mixtures of ranking models

Mixtures of ranking models are standard tools for ranking problems. However, even the fundamental question of parameter identifiability is not fully understood: the identifiability of a mixture model with two Bradley-Terry-Luce (BTL) components has remained open. In this work, we show that popular mixtures of ranking models with two components (BTL, multinomial logistic models with slates of size 3, or Plackett-Luce) are generically identifiable, i.e., the ground-truth parameters can be identified except when they are from a pathological subset of measure zero. We provide a framework for verifying the number of solutions in a general family of polynomial systems using algebraic geometry, and apply it to these mixtures of ranking models to establish generic identifiability. The framework can be applied more broadly to other learning models and may be of independent interest.

cs.LG↗
arXiv2022

Global existence and stability of time-periodic solution to isentropic compressible Euler equations with source term

In this paper, we study the initial-boundary value problem of one-dimensional isentropic compressible Euler equations with the source term $βρ|u|^αu$. By means of wave decomposition and the uniform a-priori estimates, we prove the global existence of smooth solutions under small perturbations around the supersonic Fanno flow. Then, by Gronwall's inequality, we get the smooth solution is time-periodic.

math.AP↗
arXiv2021

Provable Training Set Debugging for Linear Regression

We investigate problems in penalized $M$-estimation, inspired by applications in machine learning debugging. Data are collected from two pools, one containing data with possibly contaminated labels, and the other which is known to contain only cleanly labeled points. We first formulate a general statistical algorithm for identifying buggy points and provide rigorous theoretical guarantees under the assumption that the data follow a linear model. We then present two case studies to illustrate the results of our general theory and the dependence of our estimator on clean versus buggy points. We further propose an algorithm for tuning parameter selection of our Lasso-based algorithm and provide corresponding theoretical guarantees. Finally, we consider a two-person "game" played between a bug generator and a debugger, where the debugger can augment the contaminated data set with cleanly labeled versions of points in the original data pool. We establish a theoretical result showing a sufficient condition under which the bug generator can always fool the debugger. Nonetheless, we provide empirical results showing that such a situation may not occur in practice, making it possible for natural augmentation strategies combined with our Lasso debugging algorithm to succeed.

cs.LG↗