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铁磁薄膜快速稳定的磁化动力学控制
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作者 李欣和 班玥 《上海大学学报(自然科学版)》 CAS CSCD 北大核心 2024年第4期758-768,共11页
提出了亚微米铁磁薄膜磁化动力学的快速控制方案.由于自旋轨道耦合作用,外加电场所激发的自旋极化电流通过s-d交换耦合引起铁磁层的局域磁矩发生偏转.使用量子绝热捷径技术反控制法在亚微米铁磁薄膜模型中提出了电场控制方案,实现了磁... 提出了亚微米铁磁薄膜磁化动力学的快速控制方案.由于自旋轨道耦合作用,外加电场所激发的自旋极化电流通过s-d交换耦合引起铁磁层的局域磁矩发生偏转.使用量子绝热捷径技术反控制法在亚微米铁磁薄膜模型中提出了电场控制方案,实现了磁化向量方向快速反转,并对电场强度进行了最优化设计.另外,分析了铁磁薄膜形状各向同性和异性下的电场控制方案.相比于现有方法,该方案将磁化向量反转时间缩短了约一个数量级,并且具有更好的鲁棒性. 展开更多
关键词 铁磁性材料 磁化动力学 自旋轨道耦合 量子绝热捷径技术
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TbFeCo磁光薄膜飞秒激光感应超快磁化动力学研究 被引量:1
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作者 徐初东 翁嘉文 谭穗妍 《材料导报》 EI CAS CSCD 北大核心 2014年第2期18-20,共3页
利用时间分辨磁光克尔光谱技术,研究TbFeCo磁光薄膜飞秒激光感应超快磁化动力学过程。观测到亚皮秒的超快退磁过程,符合"三温度"模型中由电子-自旋散射引起的超快退磁机制。磁化动力学的激发功率流密度依赖关系结果表明,随着... 利用时间分辨磁光克尔光谱技术,研究TbFeCo磁光薄膜飞秒激光感应超快磁化动力学过程。观测到亚皮秒的超快退磁过程,符合"三温度"模型中由电子-自旋散射引起的超快退磁机制。磁化动力学的激发功率流密度依赖关系结果表明,随着激发功率流密度的增大,超快退磁程度增加和磁化恢复时间延长,符合"三温度"模型的解释。在衬底厚度不同的TbFeCo样品对比实验中发现,同功率流密度激发下衬底较薄的样品退磁程度更高,磁化恢复速率更快。 展开更多
关键词 TbFeCo磁光薄膜 磁化动力学 超快退磁 “三温度”模型
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电流驱动磁化动力学及其研究进展 被引量:1
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作者 郭子政 《信息记录材料》 2009年第3期45-53,共9页
电流诱发的自旋转矩效应可驱动磁矩翻转和磁畴运动,其微观机理研究是目前磁学界的一个重要的研究热点。本文介绍了巨磁电阻和隧道磁电阻效应以及其反效应自旋转矩效应的概念和原理及应用。重点介绍了电流驱动磁化动力学机制及其研究进... 电流诱发的自旋转矩效应可驱动磁矩翻转和磁畴运动,其微观机理研究是目前磁学界的一个重要的研究热点。本文介绍了巨磁电阻和隧道磁电阻效应以及其反效应自旋转矩效应的概念和原理及应用。重点介绍了电流驱动磁化动力学机制及其研究进展。对基于电流诱发的磁矩翻转原理的几种新型器件的提出、面临的主要问题以及研制的进展情况也进行了综述。 展开更多
关键词 巨磁阻 隧道磁阻 自旋转矩 电流驱动磁化动力学 赛道内存
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稀磁半导体(Ga,Mn)As薄膜激光诱导超快磁化动力学过程拟合方法探究
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作者 李杭 张新惠 《物理学报》 SCIE EI CAS CSCD 北大核心 2015年第17期313-319,共7页
本文对稀磁半导体(Ga,Mn)As薄膜中超快激光诱导磁化动力学响应信号的不同拟合方法进行了对比分析.通过Landau-Lifshitz-Gilbert(LLG)方程的数值拟合发现,由于薄膜平面内和平面外磁光响应强度不同,磁矢量三维进动的叠加可以导致多个频率... 本文对稀磁半导体(Ga,Mn)As薄膜中超快激光诱导磁化动力学响应信号的不同拟合方法进行了对比分析.通过Landau-Lifshitz-Gilbert(LLG)方程的数值拟合发现,由于薄膜平面内和平面外磁光响应强度不同,磁矢量三维进动的叠加可以导致多个频率振动模式的假象.当使用高于(Ga,Mn)As带边的能量激发时,磁化进动的磁光响应信号中叠加着来自光极化载流子的响应,此时单纯利用LLG方程对薄膜整体磁化动力学过程拟合应谨慎使用.本工作为正确分析和理解脉冲激光对(Ga,Mn)As铁磁性的超快调控提供了拟合方法上的指导. 展开更多
关键词 磁化动力学 (Ga Mn)As 时间分辨磁光克尔效应
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激光辅助跨越补偿点磁化反转动力学的实验测量
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作者 陈志峰 方晓惠 +1 位作者 徐毅 吴羽 《广州大学学报(自然科学版)》 CAS 2014年第2期42-47,共6页
文章介绍了稀土-过渡族金属铁磁合金薄膜的磁学性质以及超快磁化动力学的一般测量方法,论述了传统实验手段难以测量非可逆的激光辅助跨越补偿点磁化反转动力学的原因.实现了一种新的实验测量方法——光-磁同步动态磁光测量法,并论述了... 文章介绍了稀土-过渡族金属铁磁合金薄膜的磁学性质以及超快磁化动力学的一般测量方法,论述了传统实验手段难以测量非可逆的激光辅助跨越补偿点磁化反转动力学的原因.实现了一种新的实验测量方法——光-磁同步动态磁光测量法,并论述了相关原理和技术.以此方法测量得到了GdFeCo薄膜的磁化反转动力学,能够反映真正跨越补偿点磁光记录的过程信息. 展开更多
关键词 磁化动力学 磁光记录 跨越补偿点
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CoFe矩形纳米点的动力学反磁化特性研究
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作者 张光富 郭晓 张学军 《湖南城市学院学报(自然科学版)》 CAS 2015年第3期85-88,共4页
采用微磁学模拟方法研究了CoFe矩形纳米点在方波脉冲场作用下的动力学反磁化过程。研究发现,CoFe矩形纳米点S形微磁结构的反磁化特性与脉冲场强有着密切的关系。存在两种不同的动态反磁化过程。场强较弱时,反磁化首先在磁体两末端及磁... 采用微磁学模拟方法研究了CoFe矩形纳米点在方波脉冲场作用下的动力学反磁化过程。研究发现,CoFe矩形纳米点S形微磁结构的反磁化特性与脉冲场强有着密切的关系。存在两种不同的动态反磁化过程。场强较弱时,反磁化首先在磁体两末端及磁体中央分别形反磁化核,而后两边缘畴壁移动到磁体中部重合并逐渐由中间开始向上下两边收缩而消失,完成反磁化过程。场强较大时,反磁化过程中边缘畴壁的磁结构发生变化,逐渐由类似180o的畴壁向类似360o的畴壁转变,导致畴壁移动速度的减缓或被钉扎住。反磁化过程转变为360o畴壁的收缩湮灭过程。由于脉冲场强引起畴壁结构的变化导致反磁化时间随场强的变化表现出非单调减小的趋势。 展开更多
关键词 磁纳米点 动力学磁化过程 磁化时间 微磁学
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磁性材料超快动力学研究与飞秒抽运探测技术
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作者 翁孟超 陈磊 杨志强 《材料导报》 EI CAS CSCD 北大核心 2007年第6期112-115,共4页
阐述了磁性材料的重要性及其超快过程研究中存在的问题,对飞秒抽运探测(Pump-probe)技术的试验方法和原理进行了论述。介绍了飞秒抽运探测技术对磁性材料中磁化动力学过程的研究现状,以及抽运探测在磁性材料研究中的新发展——对磁致伸... 阐述了磁性材料的重要性及其超快过程研究中存在的问题,对飞秒抽运探测(Pump-probe)技术的试验方法和原理进行了论述。介绍了飞秒抽运探测技术对磁性材料中磁化动力学过程的研究现状,以及抽运探测在磁性材料研究中的新发展——对磁致伸缩材料中的磁化动力学过程研究、对材料复介电常数的测定和光学探针技术的引入,为磁性材料的应用和磁化动力学研究提供了新的方向。 展开更多
关键词 飞秒激光 抽运探测 磁性薄膜 磁化动力学
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矩形磁性纳米点动力学反磁化过程的微磁学研究 被引量:4
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作者 宋三元 郭光华 +1 位作者 张光富 宋文斌 《物理学报》 SCIE EI CAS CSCD 北大核心 2009年第8期5757-5762,共6页
采用微磁学模拟方法研究了初始态为C形磁结构的矩形CoFe纳米点在方波脉冲场作用下的动力学反磁化过程.研究发现,随着脉冲场强的增强,磁体的反磁化模式发生了改变.当场强较弱时反磁化过程通过畴壁移动-单涡旋的形成和移动来完成;当场强... 采用微磁学模拟方法研究了初始态为C形磁结构的矩形CoFe纳米点在方波脉冲场作用下的动力学反磁化过程.研究发现,随着脉冲场强的增强,磁体的反磁化模式发生了改变.当场强较弱时反磁化过程通过畴壁移动-单涡旋的形成和移动来完成;当场强较大时反磁化过程模式转变为畴壁移动-双涡旋的形成与移动;在更强的场强下反磁化过程通过畴壁的移动-多涡旋的形成与湮没来实现.由于反磁化模式随场强的变化而改变,反磁化时间随场强的增大出现振荡变化现象. 展开更多
关键词 动力学磁化过程 磁化时间 微磁学模拟
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Fe_(3)O_(4)/Au单晶异质结的磁各向异性研究
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作者 胡偲聪 庄铭哲 +3 位作者 雷明月 刘文文 刘二 徐锋 《南京理工大学学报》 CAS CSCD 北大核心 2024年第1期112-117,共6页
基于铁磁/重金属异质结结构的纯自旋流电子器件具有低功耗、非易失性等优点,是当前自旋电子学研究的核心内容。该文利用超导量子干涉仪以及铁磁共振测量系统等手段,对分子束外延法生长的铁磁/重金属异质结Fe_(3)O_(4)/Au单晶薄膜的静态... 基于铁磁/重金属异质结结构的纯自旋流电子器件具有低功耗、非易失性等优点,是当前自旋电子学研究的核心内容。该文利用超导量子干涉仪以及铁磁共振测量系统等手段,对分子束外延法生长的铁磁/重金属异质结Fe_(3)O_(4)/Au单晶薄膜的静态及动态磁性能进行了系统研究。研究表明,随薄膜厚度的增加,Fe_(3)O_(4)的单轴磁各向异性逐渐减小而磁晶各向异性逐渐增强。Au覆盖层的引入有助于单晶超薄膜的晶格弛豫,进而有效增强了Fe_(3)O_(4)的磁各向异性。该研究为铁磁/重金属异质结的构建提供了新的思路,有望推动其在纯自旋流电子器件中的实用化进程。 展开更多
关键词 Fe_(3)O_(4)单晶 铁磁/重金属异质结 磁各向异性 铁磁共振 磁化动力学
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Siderite pyrolysis in suspension roasting:An in-situ study on kinetics,phase transformation,and product properties 被引量:3
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作者 ZHANG Qi SUN Yong-sheng +2 位作者 QIN Yong-hong GAO Peng YUAN Shuai 《Journal of Central South University》 SCIE EI CAS CSCD 2022年第6期1749-1760,共12页
Siderite,as an abundant iron ore,has not been effectively utilized,with a low utilization rate.In this study,the in-situ kinetics and mechanism of siderite during suspension magnetization roasting(SMR)were investigate... Siderite,as an abundant iron ore,has not been effectively utilized,with a low utilization rate.In this study,the in-situ kinetics and mechanism of siderite during suspension magnetization roasting(SMR)were investigated to improve the selective conversion of siderite to magnetite and CO,enriching the theoretical system of green SMR using siderite as a reductant.According to the gas products analyses,the peak value of the reaction rate increased with increasing temperature,and its curves presented the feature of an early peak and long tail.The mechanism function of the siderite pyrolysis was the contraction sphere model(R_(3)):f(α)=3(1−α)2/3;E_(α)was 46.4653 kJ/mol;A was 0.5938 s^(−1);the kinetics equation was k=0.5938exp[−46.4653/(RT)].The in-situ HT-XRD results indicated that siderite was converted into magnetite and wüstite that exhibited a good crystallinity in SMR under a N_(2) atmosphere.At 620℃,the saturation magnetization(M_(s)),remanence magnetization(Mr),and coercivity(Hc)of the product peaked at 53.63×10^(-3)A·m^(2)/g,10.23×10^(-3)A·m^(2)/g,and 12.40×10^(3)A/m,respectively.Meanwhile,the initial particles with a smooth surface were transformed into particles with a porous and loose structure in the roasting process,which would contribute to reducing the grinding cost. 展开更多
关键词 SIDERITE suspension magnetization roasting reaction kinetics phase transformation magnetic transition microstructure evolution
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Three-dimensional unsteady squeezing flow with irreversibility 被引量:2
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作者 HAYAT T AHMAD M Waqar +1 位作者 SHEHZAD S A ALSAEDI A 《Journal of Central South University》 SCIE EI CAS CSCD 2021年第11期3368-3380,共13页
This exploration examines unsteady magnetohydrodynamic(MHD) three-dimensional flow of viscous material between rotating plates subject to radiation,Joule heating and chemical reaction.The non-linear partial differenti... This exploration examines unsteady magnetohydrodynamic(MHD) three-dimensional flow of viscous material between rotating plates subject to radiation,Joule heating and chemical reaction.The non-linear partial differential system is re-structured into the ordinary differential expressions by the implication of appropriate transformations.The developed differential equations are computed by homotopy analysis technique.Numerical consequences have been accomplished by various values of emerging parameters.Coefficients of skin friction and heat and mass transfer rates have been scrutinized.Irreversibility analysis is carried out.Influence of various prominent variables on entropy generation is presented.Moreover,the temperature increases for higher Dufour number and concentration distribution reduces against Soret number.Higher squeezing parameter enhances velocity while concentration reduces with an increment in squeezing parameter.Both entropy rate and Bejan number increase against higher diffusion parameter. 展开更多
关键词 Joule heating viscous dissipation magnetohydrodynamic(MHD)flow chemical reaction entropy generation
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Magneto-hydrodynamic flow of squeezed fluid with binary chemical reaction and activation energy 被引量:2
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作者 S.AHMAD M.FAROOQ +2 位作者 N.A.MIR Aisha ANJUM M.JAVED 《Journal of Central South University》 SCIE EI CAS CSCD 2019年第5期1362-1373,共12页
The present exploration is conducted to describe the motion of viscous fluid embedded in squeezed channel under the applied magnetics effects.The processes of heat and mass transport incorporate the temperature-depend... The present exploration is conducted to describe the motion of viscous fluid embedded in squeezed channel under the applied magnetics effects.The processes of heat and mass transport incorporate the temperature-dependent binary chemical reaction with modified Arrhenius theory of activation energy function which is not yet disclosed for squeezing flow mechanism.The flow,heat and mass regime are exposed to be governed via dimensionless,highly non-linear,ordinary differential equations (ODEs) under no-slip walls boundary conditions.A well-tempered analytical convergent procedure is adopted for the solutions of boundary value problem.A detailed study is accounted through graphs in the form of flow velocity field,temperature and fluid concentration distributions for various emerging parameters of enormous interest.Skin-friction,Nusselt and Sherwood numbers have been acquired and disclosed through plots.The results indicate that fluid temperature follows an increasing trend with dominant dimensionless reaction rate σ and activation energy parameter E.However,an increment in σ and E parameters is found to decline in fluid concentration.The current study arises numerous engineering and industrial processes including polymer industry,compression and injection shaping,lubrication system,formation of paper sheets,thin fiber,molding of plastic sheets.In the area of chemical engineering,geothermal engineering,cooling of nuclear reacting,nuclear or chemical system,bimolecular reactions,biochemical process and electrically conducting polymeric flows can be controlled by utilizing magnetic fields.Motivated by such applications,the proposed study has been developed. 展开更多
关键词 squeezing flow magneto-hydrodynamics (MHD) activation energy binary chemical reaction
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Waveforms analysis and optimization of new electro-hydraulic excitation technology 被引量:3
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作者 韩冬 龚国芳 +2 位作者 杨华勇 刘毅 廖湘平 《Journal of Central South University》 SCIE EI CAS 2014年第8期3098-3106,共9页
A new electro-hydraulic exciter that consists of rotary valve and micro-displacement double-functioned hydraulic cylinder was proposed to realize different kinds of waveforms.Calculated fluid dynamics(CFD) simulation ... A new electro-hydraulic exciter that consists of rotary valve and micro-displacement double-functioned hydraulic cylinder was proposed to realize different kinds of waveforms.Calculated fluid dynamics(CFD) simulation of rotary valve orifice reveals that orifice exists the two-throttle phenomenon.According to the finding,the revised flow area model was established.Vibration waveforms analysis was carried out by means of mathematic model and the related experiments were validated.Furthermore,as a new analysis indicator,saturation percentage was introduced first.The experimental results indicate that the revised flow area model is more accurate compared to the original one,and vibration waveforms can be optimized through suitable spool parameters and the revised cylinder structure. 展开更多
关键词 rotary valve micro-displacement double-functioned hydraulic cylinder two-throttle phenomenon revised flow areamodel saturation drift motion
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Magnetic Nano-Amorphous-Iron-Oxide-Based Drug Delivery System with Dual Therapeutic Mechanisms
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作者 Shan Lei Li-an Wang +3 位作者 Fu-xing Lin Kun Zeng Mo-zhen Wang Xue-wu Ge 《Chinese Journal of Chemical Physics》 SCIE CAS CSCD 2020年第3期376-384,I0003,共10页
Smart nanoparticles that respond to pathophysiological parameters,such as p H,GSH,and H2O2,have been developed with the huge and urgent demand for the high-efficient drug delivery systems(DDS)for cancer therapy.Herein... Smart nanoparticles that respond to pathophysiological parameters,such as p H,GSH,and H2O2,have been developed with the huge and urgent demand for the high-efficient drug delivery systems(DDS)for cancer therapy.Herein,cubic poly(ethylene glycol)(PEG)-modified mesoporous amorphous iron oxide(AFe)nanoparticles(AFe-PEG)have been successfully prepared as p H-stimulated drug carriers,which can combine doxorubicin(DOX)with a high loading capacity of 948 mg/g,forming a novel multifunctional AFe-PEG/DOX nanoparticulate DDS.In an acidic microenvironment,the AFe-PEG/DOX nanoparticles will not only release DOX efficiently,but also release Fe ions to catalyze the transformation of H2O2 to·OH,acting as fenton reagents.In vitro experimental results proved that the AFe-PEG/DOX nanoparticles can achieve combination of chemotherapeutic(CTT)and chemodynamic therapeutic(CDT)effects on Hela tumor cells.Furthermore,the intrinsic magnetism of AFePEG/DOX makes its cellular internalization efficiency be improved under an external magnetic field.Therefore,this work develops a new and promising magnetically targeted delivery and dual CTT/CDT therapeutic nano-medicine platform based on amorphous iron oxide. 展开更多
关键词 Cubic amorphous iron oxide nanoparticles p H-responsive CHEMOTHERAPY Chemodynamic therapy Magnetically targeted delivery
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Effect of Static Magnetic Field on α-Amylase Activity and Enzymatic Reaction 被引量:1
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作者 贾绍义 刘勇 +1 位作者 吴松海 王志斌 《Transactions of Tianjin University》 EI CAS 2009年第4期272-275,共4页
The effect of magnetic field on a-amylase was studied. Under the experimental conditions, a-amylase solution was treated by 0.15 T, 0.30 T and 0.45 T static magnetic fields for a known period of time, then the activit... The effect of magnetic field on a-amylase was studied. Under the experimental conditions, a-amylase solution was treated by 0.15 T, 0.30 T and 0.45 T static magnetic fields for a known period of time, then the activity, kinetic parameters, and the secondary conformation were investigated. The results showed that there was a considerable effect of the magnetic exposure on the α-amylase. The activity was increased by 27%, 34.1%, 37.8% compared with the control. It was also found that both kinetic parameters Km and Vm could be decreased due to the increasing magnetic field, Km decreased from 2.20×10^2 to 0.87×10^2, whereas Vm decreased from 2.0×10^3 g/min to 1.1 ×10^3 g/min. At the same time, there were some irregular changes in a-amylase secondary conformation. 展开更多
关键词 static magnetic field or-amylase ACTIVITY secondary conformation Michaelis constant
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Susceptibilities of QCD Vacuum from Renormalized Dyson-Schwinger Equations]
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作者 CHENWei QIShi +1 位作者 SUNWei-Min ZONGHong-Shi 《Communications in Theoretical Physics》 SCIE CAS CSCD 2004年第6期917-920,共4页
The pion and tensor vacuum susceptibilities are calculated in the framework of the renormalizable DysonSchwinger equations. A comparison with the results of other nonperturbative QCD approaches is given.
关键词 QCD vacuum vacuum susceptibility Dyson-Schwinger equations
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Janus γ-Fe2O3/SiO2-based nanotheranostics for dual-modal imaging and enhanced synergistic cancer starvation/chemodynamic therapy 被引量:7
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作者 Yifan Zhang Yilin Wan +8 位作者 Yunyan Liao Yanjie Hu Tao Jiang Ting He Wei Bi Jing Lin Peng Gong Longhua Tang Peng Huang 《Science Bulletin》 SCIE EI CAS CSCD 2020年第7期564-572,M0004,共10页
Multimodal cancer synergistic therapy exhibited remarkable advantages over monotherapy in producing an improved therapeutic efficacy. In this work, Janus-type γ-Fe2 O3/SiO2 nanoparticles(JFSNs) are conjugated with gl... Multimodal cancer synergistic therapy exhibited remarkable advantages over monotherapy in producing an improved therapeutic efficacy. In this work, Janus-type γ-Fe2 O3/SiO2 nanoparticles(JFSNs) are conjugated with glucose oxidase(GOx) for synergistic cancer starvation/chemodynamic therapy. The γ-Fe2O3 hemisphere of JFSNs can perform photoacoustic/T2 magnetic resonance dual-modal imaging of tumors.GOx on the surface of JFSNs catalyzes the decomposition of glucose and produces H2O2 for cancer starvation therapy. Subsequently, the γ-Fe2O3 hemisphere catalyzes the disproportionation of H2O2 to generate highly reactive hydroxyl radicals in an acidic tumor microenvironment. The close distance between GOx and JFSNs ensures adequate contact between the γ-Fe2O3 hemisphere and its substrate H2O2, thus enhancing the catalytic efficiency. This synergy of glucose depletion, biotoxic H2O2 and hydroxyl radicals significantly suppresses 4 T1 mammary tumor growth with minimal adverse effects. 展开更多
关键词 Synergistic therapy Janus nanoparticles Glucose oxidase Fenton-like reaction THERANOSTICS
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Dynamics of Charged Particles Around a Magnetized Black Hole with Pseudo–Newtonian Potential
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作者 王颖 伍歆 孙威 《Communications in Theoretical Physics》 SCIE CAS CSCD 2013年第10期433-438,共6页
The linear stability of equilibria of charged particles moving near a compact object with a dipole magnetic field and a pseudo-Newtonian potential is analyzed detalledly. An optimal fourth-order force gradient symplec... The linear stability of equilibria of charged particles moving near a compact object with a dipole magnetic field and a pseudo-Newtonian potential is analyzed detalledly. An optimal fourth-order force gradient symplectic method, as a global symplectic integrator that can simultaneously solve both the equations of motion and the variational equations, is used to calculate fast Lyapunov indicators. In this way, dynamical structures are described, and parameter domains for causing chaos are found. 展开更多
关键词 pseudo-Newtonian potential CHAOS symplectic integrator
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Doubled conformal compactification
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作者 SUN ZhaoYong TIAN Yu 《Science China(Physics,Mechanics & Astronomy)》 SCIE EI CAS 2014年第9期1630-1636,共7页
We use Weyl transformations between the Minkowski spacetime and dS/AdS spacetime to show that one cannot well define the electrodynamics globally on the ordinary conformal compactification of the Minkowski spacetime(o... We use Weyl transformations between the Minkowski spacetime and dS/AdS spacetime to show that one cannot well define the electrodynamics globally on the ordinary conformal compactification of the Minkowski spacetime(or dS/AdS spacetime),where the electromagnetic field has a sign factor(and thus is discountinuous)at the light cone.This problem is intuitively and clearly shown by the Penrose diagrams,from which one may find the remedy without too much difficulty.We use the Minkowski and dS spacetimes together to cover the compactified space,which in fact leads to the doubled conformal compactification.On this doubled conformal compactification,we obtain the globally well-defined electrodynamics. 展开更多
关键词 conformal transformations ELECTRODYNAMICS doubled Penrose diagrams conformal compactification
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