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Stability of the Wulff shape with respect to anisotropic curvature functionals

JOURNAL OF FUNCTIONAL ANALYSIS 2025年第3期288卷

作者： Scheuer, Julian zhang, xuwen Goethe Univ Inst Math Robert Mayer Str 10 D-60325 Frankfurt Germany Univ Freiburg Math Inst Ernst Zermelo Str 1 D-79104 Freiburg Germany

For a function f which foliates a one-sided neighborhood of a closed hypersurface M, we give an estimate of the distance of M to a Wulff shape in terms of the Lp-norm of the traceless F-Hessian of f, where F is the support function of the Wulff shape. This theorem is applied to prove quantitative stability results for the anisotropic Heintze-Karcher inequality, the anisotropic Alexandrov problem, as well as for the anisotropic overdetermined boundary value problem of Serrin-type. (c) 2024 The Authors. Published by Elsevier Inc. This is an open access article under the CC BY license (http:// creativecommons .org /licenses /by /4 .0/).

关键词： Anisotropic curvature conditions Anisotropic overdetermined problem

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Experimental and numerical investigation on the tensile behaviour of rocks using the Brazilian disc method

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JOURNAL OF APPLIED GEOPHYSICS 2025年 233卷

作者： Chen, Yulong zhang, xuwen Yuan, Honghui zhang, Junwen China Coal Res Inst Beijing 100013 Peoples R China China Univ Min & Technol Beijing Beijing 100083 Peoples R China

Characterizing engineering properties of rock especially associated with tension is crucial for stability assessment of rock structures. This study integrates physical and numerical experiments to investigate the electromagnetic radiation (EMR) and acoustic emission (AE) responses of sandstone under Brazilian disc testing. During the Brazilian splitting process, the EMR and AE responses reflect well the cracking evolution of the disc sandstone specimen. The cracking evolution process and failure mechanism are vividly illustrated. When approaching the peak stress, massive EMR and AE activities occur abruptly. Importantly, the fractal dimension and b-value of EMR and AE switch from increase to decrease once the failure initiates. Such significant decrease in the fractal dimension and b-value of EMR and AE upon failure initiation could be applied to identify the rock failure initiation.

关键词： EMR AE Brazilian disc Cracking Fractal dimension B-value

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A CHARACTERIZATION OF CAPILLARY SPHERICAL CAPS BY A PARTIALLY OVERDETERMINED PROBLEM IN A HALF BALL

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PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY 2025年第1期153卷 161-170页

作者： Jia, Xiaohan Lu, Zheng Xia, Chao zhang, xuwen Southeast Univ Sch Math Nanjing 211189 Peoples R China Xiamen Univ Sch Math Sci Xiamen 361005 Peoples R China Albert Ludwigs Univ Freiburg Math Inst D-79104 Freiburg Germany Goethe Univ Inst Math D-60325 Frankfurt Germany Univ Freiburg Math Inst Ernst Zermelo Str1 D-79104 Freiburg Germany

In this paper, we study a Serrin-type partially overdetermined problem proposed by Guo-Xia [Calc. Var. Partial Differential Equations (2019), Paper No. 160, 15], and prove a rigidity result that characterizes capillar... 详细信息

关键词： Key words and phrases. Serrin's overdetermined problem mixed boundary value problem capillary hypersurfaces. capillary hypersurfaces

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Willmore-type inequality in unbounded convex sets

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JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES 2025年第3期111卷

作者： Jia, Xiaohan Wang, Guofang Xia, Chao zhang, xuwen Southeast Univ Sch Math Nanjing Peoples R China Univ Freiburg Math Inst Ernst Zermelo Str1 D-79104 Freiburg Germany Xiamen Univ Sch Math Sci Xiamen Peoples R China

In this paper, we prove the following Willmore-type inequality: on an unbounded closed convex set K subset of Rn+1$K\subset \mathbb {R}{n+1}$ (n >= 2$(n\geqslant 2$), for any embedded hypersurface Sigma subset of K...

In this paper, we prove the following Willmore-type inequality: on an unbounded closed convex set K subset of Rn+1$K\subset \mathbb {R}<^>{n+1}$ (n >= 2$(n\geqslant 2$), for any embedded hypersurface Sigma subset of K${\Sigma }\subset K$ with boundary partial derivative Sigma subset of partial derivative K$\partial {\Sigma }\subset \partial K$ satisfying a certain contact angle condition, there holds 1n+1 integral Sigma HndA >= AVR(K)|Bn+1|.$$\begin{equation*} {\frac{1}{n+1}\int _{{\Sigma }}{\left|{H}\right|}<^>n d A\geqslant \rm AVR}(K)\vert \mathbb {B}<^>{n+1}\vert . \end{equation*}$$Moreover, equality holds if and only if Sigma${\Sigma }$ a part of a sphere and K\Omega$K\setminus \Omega$ is a part of the solid cone determined by Sigma${\Sigma }$. Here, Omega$\Omega$ is the bounded domain enclosed by Sigma${\Sigma }$ and partial derivative K$\partial K$, H$H$ is the normalized mean curvature of Sigma${\Sigma }$, and AVR(K)${\rm AVR}(K)$ is the asymptotic volume ratio of K$K$. We also prove an anisotropic version of this Willmore-type inequality. As a special case, we obtain a Willmore-type inequality for anisotropic capillary hypersurfaces in a half-space.

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Energy Driving-Damage Degradation-Structural Failure Mechanism of Layered Sandstones Under Uniaxial Conditions

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ROCK MECHANICS AND ROCK ENGINEERING 2025年第3期58卷 3815-3853页

作者： Song, Zhixiang zhang, Junwen Wu, Shaokang Zhao, Shankun zhang, Yang Dong, Xukai zhang, xuwen Wang, Sihe China Univ Min & Technol Beijing Sch Energy & Min Engn Beijing 100083 Peoples R China China Coal Res Inst Mine Safety Technol Branch Beijing 100013 Peoples R China

It is of great theoretical significance to effectively reveal the energy driving-damage degradation-structural failure mechanism of rocks for the probability evaluation and prevention of rock burst in deep coal mines. Therefore, uniaxial loading and unloading tests of layered sandstones were conducted. Subsequently, the progressive failure process and stress-strain curves were obtained. Then, the evolution characteristics of strength, strain, energy, damage and macroscopic failure was characterized. Meanwhile, the damage proportion at each stage was quantified, and the linear damage deterioration law was obtained. Finally, the energy driving-damage degradation-structural failure mechanism was revealed. The results showed that: (1) increasing the unloading stress level did not necessarily reduce the bearing capacity, but the unloading effect could significantly affect the energy storage capacity;(2) there was the significant linear evolution relationship between the damage proportion and the unloading stress level under identical inclination angle in stages II and IV;(3) When the unloading stress level was over 0.7, the pre-peak structural adjustment behavior could strengthen the stability of post-peak structures and reduce the impact degree of rock burst. The conclusions could provide certain of theoretical basis for the prevention of rock burst in deep coal mines.

关键词： Structural evolution Unloading stress level Linear damage deterioration law Energy driving-damage degradation-structural failure mechanism Rock burst

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COMPACTNESS OF CAPILLARY HYPERSURFACES WITH MEAN CURVATURE PRESCRIBED BY AMBIENT FUNCTIONS

arXiv

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arXiv 2025年

作者： zhang, xuwen Mathematisches Institut Universität Freiburg Ernst-Zermelo-Str.1 Freiburg79104 Germany

We prove a compactness result for capillary hypersurfaces with mean curvature prescribed by ambient functions, which generalizes the results of Schätzle [17] and Bellettini [4] to the capillary case. The proof relies on extending the definition of (unoriented) curvature varifolds with capillary boundary introduced by Wang-zhang [19] to the context of oriented integral varifolds. We also discuss the case when the mean curvature of the boundary is prescribed. MSC 2020: 49Q15, 53C42MSC Codes 49Q15, 53C42 Copyright © 2025, The Authors. All rights reserved.

关键词： Capillarity

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VARIFOLDS WITH CAPILLARY BOUNDARY

arXiv

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arXiv 2025年

作者： Wang, Guofang zhang, xuwen Mathematisches Institut Universität Freiburg Ernst-Zermelo-Str.1 Freiburg79104 Germany

In this paper we introduce and study a new class of varifolds in Rn+1 of arbitrary dimensions and co-dimensions, which satisfy a Neumann-type boundary condition characterizing capillarity. The key idea is to introduce a Radon measure on a subspace of the trivial Grassmannian bundle over the supporting hypersurface as a generalized boundary with prescribed angle, which plays a role as a measure-theoretic capillary boundary. We show several structural properties, monotonicity inequality, boundary rectifiability, classification of tangent cones, and integral compactness for such varifolds under reasonable conditions. This Neumann-type boundary condition fits very well in the context of curvature varifold and Brakke flow, which we also *** Codes 49Q15, 53C42 Copyright © 2025, The Authors. All rights reserved.

关键词： Boundary conditions

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Boosting catalytic performance of N doped porous carbon derived from coal tar pitch: The role of N species and the contribution of 1O2

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JOURNAL OF WATER PROCESS ENGINEERING 2025年 72卷

作者： Huang, Linlin zhang, xuwen Wang, Lin Liu, Tingting Li, Da Sheng, Tao Sun, Caiyu Li, Lixin Heilongjiang Univ Sci & Technol Coll Environm & Chem Engn Harbin 150022 Peoples R China Harbin Inst Technol State Key Lab Urban Water Resource & Environm Harbin 150090 Peoples R China

In this study, nitrogen-doped carbon material (N-PC-d) derived from coal tar pitch using dicyandiamide as N source was successfully synthesized, exhibiting outstanding catalytic performance in the activation of peroxymonosulfate (PMS) for the degradation of Orange G (OG). By optimizing key parameters such as PMS dosage, NPC dosage, nitrogen source, pH, anions, and PS source, the optimal N-PC-d/PMS system achieved a degradation rate 1.45 times higher than that of the PC/PMS system within a broad pH range (2.0-10.0). Through electron paramagnetic resonance (EPR) and quenching experiments, it was found that singlet oxygen (1O2) was the predominant species accountable for OG degradation, while reactive oxygen species (ROS), including superoxide (O2 & sdot;-), hydroxyl radicals (& sdot;OH), and sulfate radicals (SO4 & sdot;-), played auxiliary roles. Moreover, the structure-activity relationship analysis revealed that functional groups such as C--C, C--O, and pyridine N were mainly involved in PMS activation. The degradation mechanism of OG was further elucidated by high-performance liquid chromatography-mass spectrometry (HPLC-MS). This research presented a cost-efficient N-doped porous carbon material for environmental remediation and provides more profound insights into the mechanisms of PMS activation by N doped carbon-based materials.

关键词： N-doped porous carbon Coal tar pitch PMS Singlet oxygen Orange G

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Metal-Organic Frameworks-Derived Cobalt Catalyst Supported on Biochar for Efficient Deoxygenation of Stearic Acid

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INDUSTRIAL & ENGINEERING CHEMISTRY RESEARCH 2025年第4期64卷 2049-2060页

作者： zhang, xuwen Dong, Xuexue Wang, Youting Bian, Juanjuan Ali, Sajid Cai, Dongren Sun, Kang Rao, Xiaoping Jiang, Jianchun Zhan, Guowu Huaqiao Univ Acad Adv Carbon Convers Technol Coll Chem Engn Xiamen 361021 Fujian Peoples R China Huaqiao Univ Fujian Prov Key Lab Biomass Low Carbon Convers Xiamen 361021 Fujian Peoples R China Chinese Acad Forestry CAF Inst Chem Ind Forest Prod Nanjing 210042 Jiangsu Peoples R China

The conversion of stearic acid into linear hydrocarbons is a crucial step in advancing sustainable biofuels and biochemicals. Herein, we developed a series of cobalt-based catalysts (referred to as Co/C@TSC) using metal-organic frameworks (MOFs) as precursors and supporting them on biochar derived from natural tung shells (TSC). Tung shells, a byproduct of the tung oil extraction process, are widely available. The as-designed Co/C@TSC catalyst effectively deoxygenated stearic acid via decarbonylation/decarboxylation (DCO x ) processes, achieving a conversion of 78.5% and hydrocarbon product selectivity of 90%, specifically heptadecane and heptadecene. Our detailed analysis showed that the addition of biochar support improved the spatial distribution of cobalt species (with a high surface concentration of Co0) and enhanced the adsorption of reactants, thus boosting catalytic activity. Additionally, in situ DRIFTS analysis confirmed that the stearic acid deoxygenation process involved the intermolecular dehydration of stearic acid molecules. Experiments with different reaction substrates revealed that the stearic anhydride was a key reaction intermediate during the deoxygenation process. This study introduces a novel catalyst made from dual carbon-supported nonprecious metals, presenting a promising method for transforming stearic acid into valuable hydrocarbon products.

关键词： Reaction intermediates

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Harnessing conversion bridge strategy by organic semiconductor in polymer matrix memristors for high-performance multi-modal neuromorphic signal processing

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INFOMAT 2025年第5期7卷

作者： Dong, Weijia Ji, Xuan An, Chuanbin Xu, Chenhui zhang, xuwen Zhao, Bin Liu, Yuqian Wang, Shiyu Yu, Xi Liu, Xinjun Han, Yang Geng, Yanhou Tianjin Univ Sch Mat Sci & Engn Tianjin Key Lab Mol Optoelect Sci Minist EducCollaborat Innovat Ctr Chem Sci & Engn Tianjin 300350 Peoples R China Tianjin Univ Collaborat Innovat Ctr Chem Sci & Engn Tianjin Key Lab Organ Integrated Circuits Minist Educ Tianjin Peoples R China Tianjin Univ Sch Sci Dept Chem Key Lab Organ Integrated CircuitMinist Educ Tianjin 300072 Peoples R China Tianjin Univ Sch Sci Dept Chem Tianjin Key Lab Mol Optoelect Sci Tianjin 300072 Peoples R China Tianjin Univ Joint Sch Natl Univ Singapore & Tianjin Univ Int Campus Fuzhou Peoples R China Trina Solar State Key Lab Photovolta Sci & Technol Changzhou Peoples R China Tianjin Univ Fac Sci Tianjin Key Lab Low Dimens Mat Phys & Preparat Tec Tianjin 300354 Peoples R China

Organic memristors, integrating chemically designed resistive switching and mechanical flexibility, present promising hardware opportunities for neuromorphic computing, particularly in the development of next-generation wearable artificial intelligence devices. However, challenges persist in achieving high yield, controllable switching, and multi-modal information processing. In this study, we introduce an efficient distribution of conversion bridges (EDCB) strategy by dispersing organic semiconductor (poly[2,5-bis(3-tetradecylthiophen-2-yl)thieno[3,2-b]thiophene], PBTTT) in elastomer (polystyrene-block-poly(ethylene-ran-butylene)-block-polystyrene, SEBS). This innovative approach results in memristors with exceptional yield, high stretchability, and reliable switching performance. By fine-tuning the semiconductor content, we shift the primary charge carriers from ions to electrons, realizing modulable non-volatile, and volatile duo-mode memristors. This advancement enables multi-modal signal processing at distinct operational mechanisms-non-volatile mode for image recognition in convolutional neural networks (CNNs) and volatile mode for dynamic classification and prediction in reservoir computing (RC). A fully analog RC hardware system is further demonstrated by integrating the distinct volatile and non-volatile modes of the EDCB-based memristor into the dynamic neuron network and the linear regression layer of the RC respectively, achieving high accuracy in online arrhythmia detection tasks. Our work paves the way for high-yield organic memristors with mechanical flexibility, advancing efficient multi-mode neuromorphic computing within a unified memristor system integrating volatile and non-volatile ***

关键词： convolutional neural network neuromorphic computing organic memristors reservoir computing stretchable electronics

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