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Furnace Temperature Curve Optimization Model Based on Differential Evolution Algorithm
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作者 Yiming Cheng 《Journal of Electronic Research and Application》 2024年第4期64-80,共17页
When soldering electronic components onto circuit boards,the temperature curves of the reflow ovens across different zones and the conveyor belt speed significantly influence the product quality.This study focuses on ... When soldering electronic components onto circuit boards,the temperature curves of the reflow ovens across different zones and the conveyor belt speed significantly influence the product quality.This study focuses on optimizing the furnace temperature curve under varying settings of reflow oven zone temperatures and conveyor belt speeds.To address this,the research sequentially develops a heat transfer model for reflow soldering,an optimization model for reflow furnace conditions using the differential evolution algorithm,and an evaluation and decision model combining the differential evolution algorithm with the Technique for Order Preference by Similarity to Ideal Solution(TOPSIS)method.This approach aims to determine the optimal furnace temperature curve,zone temperatures of the reflow oven,and the conveyor belt speed. 展开更多
关键词 Furnace temperature curve Difference equations differential evolution algorithms TOPSIS methods
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Differential Expression of miRNAs in Rice under High Temperature Stress 被引量:2
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作者 Guangmin XU Xiaofang YANG +2 位作者 Rong ZHANG Qiao LI Juan LI 《Agricultural Biotechnology》 CAS 2015年第4期6-9,15,共5页
The growth and development of rice are closely related with temperature. In order to clarify the mechanism of high temperature resistance in riee, in this study, using high temperature-resistant Indian rice cultivar N... The growth and development of rice are closely related with temperature. In order to clarify the mechanism of high temperature resistance in riee, in this study, using high temperature-resistant Indian rice cultivar N22 as the experimental material, Osa-rniR159c, Osa-miR159d, Osa-miR159f, Osa-miR164d, Osa- rrdR529b and Osa-miR166h-3p obtained by high-throughput sequencing as target genes, the expression patterns of these genes in young panicles of rice under high temperature stress were analyzed by RNA-tailing and primer-extension RT-PCR, which provided theoretical basis for breeding high temperature-resistant rice eultivars. 展开更多
关键词 RICE High temperature stress MIRNAS QRT-PCR differential expression
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Finite Differential Method Simulation on Temperature Field in Process of Laser Quenching 被引量:1
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作者 Gang Fan, Yihong Guan, Tieli Chen, Honggamg Wang Kunming University of Science and Technology, Kunming, 650093,China 《Journal of Shanghai Jiaotong university(Science)》 EI 2000年第1期58-62,共5页
Laser Quenching is one of main contents in laser heat treatment. At present, computer simulation on cooling course of laser quenching is the main research field and the foundation of calculating inner thermal stresses... Laser Quenching is one of main contents in laser heat treatment. At present, computer simulation on cooling course of laser quenching is the main research field and the foundation of calculating inner thermal stresses in object. It also provides theoretical basis for optimizing and controlling the course of laser quenching technology. In this paper, the difference between finite element method and finite differential method, which are two methods to calculate the laser quenching temperature field and calculation precision are studied. The unstable temperature field is solved and the configure and time are discretizcd simultaneously. About time discrete, two kinds of differential pattern are discussed. Compared the calculation results with measurement values, it shows that the differential method adopting in the paper is feasible and the calculation precision and calculation velocity can be increased to use variable step-size about time. Also, the result testifies that different calculation methods can be employed in case of variable application situation and calculation precision. 展开更多
关键词 Laser QUENCHING SIMULATION FINITE differential Method temperature FIELD
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Determination of Molecular Mass of Strong Acids by Differential Temperature Model (DTM) Using H<sub>3</sub>PO<sub>4</sub>and HBF<sub>4</sub>for Classical Demonstration
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作者 I. A. Akpan 《Journal of Materials Science and Chemical Engineering》 2015年第6期41-47,共7页
A new chemical hypothesis based on the differential temperature model (DTM) for estimation of molecular masses of some strong acids (H2SO4, HNO3 and HCl) in solutions have previously been propounded and tested theoret... A new chemical hypothesis based on the differential temperature model (DTM) for estimation of molecular masses of some strong acids (H2SO4, HNO3 and HCl) in solutions have previously been propounded and tested theoretically and analytically by the author. The results were published in the Bulletin of Pure and Applied Sciences–Chemistry in 2012. The changes in temperature following various dilutions of the acids were found to be proportional to their molecular properties. The new chemical hypothesis and model is hereby tested on H3PO4 and HBF4 and their exact molecular masses have been evaluated analytically and theoretically. The validity of the hypothesis and the model is hereby presented for chemical proof and adoption to theory by chemists. 展开更多
关键词 differential temperature Molecular Mass Strong ACIDS
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Effect of Temperature Differentials on Condensers of Split-Type Air Conditioners in Apartment Buildings
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作者 Ahmad Alotaibi Ahmad A1-Mulla Rajeev Alasseri 《Journal of Energy and Power Engineering》 2013年第2期272-276,共5页
关键词 空调冷凝器 分体式 公寓楼 温差 散热效果 空调机组 冷却能力 优化操作
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De Novo Transcriptome Analysis in Hevea brasiliensis to Unveil Genes Involved in Low Temperature Stress Response
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作者 Bingsong Yang Xiaomeng Shi +1 位作者 Tingting Guo Meixia Liang 《Phyton-International Journal of Experimental Botany》 SCIE 2023年第2期559-575,共17页
Low temperature is one of the adversities threatening the growth and development and reduces the yield of rubber trees.However,molecular mechanisms toward rubber trees in response to low temperature are largely unclea... Low temperature is one of the adversities threatening the growth and development and reduces the yield of rubber trees.However,molecular mechanisms toward rubber trees in response to low temperature are largely unclear.In this study,7,159 and 7,600 differentially expressed genes(DEGs)were identified in‘Reyan 73397’rubber trees.Through GO analysis,the catalytic activity was the representative of the GO term in the only DEGs at the two studied temperatures(room temperature and 4°C,respectively),while KEGG analysis showed that carbon metabolism was the most important grouping under the comparison of these two temperatures.In addition,expression of 9 members of transcription factor MYB family genes were further verified by qRT-PCR,and MYB family genes may play important roles in the regulation of rubber trees under low temperature stress.This study provided a theoretical foundation for(1)revealing the molecular mechanisms of rubber trees in response to low temperature and(2)breeding of tolerant varieties of rubber trees. 展开更多
关键词 Hevea brasiliensis low temperature stress TRANSCRIPTOME differential expressed genes
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New models of adipogenic differentiation highlight a cell-autonomous response to temperature
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作者 KSENIJA VELICKOVIC HILDA ANAID LUGO LEIJA +2 位作者 SARAH MCGINLAY MICHAEL ESYMONDS VIRGINIE SOTTILE 《BIOCELL》 SCIE 2020年第4期501-512,共12页
Temperature is a key regulator of brown adipose tissue(BAT)function,acting through central sensory inputs to influence metabolism and energy storage.Although animal models have produced a wealth of information on the ... Temperature is a key regulator of brown adipose tissue(BAT)function,acting through central sensory inputs to influence metabolism and energy storage.Although animal models have produced a wealth of information on the pathways,effectors and responses mediating the physiological response of adipose tissue to temperature in vivo,the use of cell culture models now offers evidence of an additional cell-autonomous response to temperature changes,in the absence of neural input.In particular,stem cell models provide new insight into the regulation of adipogenic differentiation and the induction of browning features in vitro.Here the basis for adipogenic responsiveness to low temperature is discussed,together with different human cell models available to outline the benefits of cell-based approaches for future BAT research. 展开更多
关键词 ADIPOSE tissue CELL differentiATION temperature CELL autonomous response Transient receptor potential (TRP) channels
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Effect of Different Growth State of Broccoli (Brassica oleracea var. italica) on Low Temperature Induction 被引量:4
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作者 JIANGXin-mei LIYue-fang YUXi-hong 《Journal of Northeast Agricultural University(English Edition)》 CAS 2005年第1期20-23,共4页
In order to study the responding of different growth state on low temperature in Broccoli (Brassica oleracea var. italica), we took prematurity broccoli hybrid as the objects. It was found that growth state was varied... In order to study the responding of different growth state on low temperature in Broccoli (Brassica oleracea var. italica), we took prematurity broccoli hybrid as the objects. It was found that growth state was varied under different sowing time , moreover, stem became wider with the increasing of light density at the same leaf age. Seedling age of responding to low temperature vernalization only when they grew five leaves above and with over 3.03 ±0.07 centimeter stalk width in 'Qingfeng Broccoli 103'. The older leaf age was and the stronger plant was, the more sensitive and the shorter demanded duration time on low temperature was, and the shorter time required when the plants entered into critical period of floral bud differentiation. 展开更多
关键词 BROCCOLI low temperature leaf age floral bud differentiation
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Proteomic Analysis of High Temperature Stress-Responsive Proteins in Chrysanthemum Leaves 被引量:1
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作者 Xin Li Feiya Liao +5 位作者 Qiqi Ma Beibei Jiang Yuanzhi Pan Cheng Luo Xinjie Wang Aining Ran 《Phyton-International Journal of Experimental Botany》 SCIE 2021年第5期1415-1423,共9页
Chrysanthemum is one of the most important ornamental flowers in the world,and temperature has a significant influence on its field production.In the present study,differentially expressed proteins were investigated i... Chrysanthemum is one of the most important ornamental flowers in the world,and temperature has a significant influence on its field production.In the present study,differentially expressed proteins were investigated in the leaves of Dendranthema grandiflorum‘Jinba’under high temperature stress using label-free quantitative proteomics techniques.The expressed proteins were comparatively identified and analyzed.A total of 1,463 heat-related,differentially expressed proteins were successfully identified by Liquid Chromatography-tandem Mass Spectrometry(LC-MS/MS),and 1,463 heat-related,differentially expressed proteins were successfully identified by mass spectrometry after a high temperature treatment.Among these,701 proteins were upregulated and 762 proteins were downregulated.The in-depth bioinformatics analysis of these differentially expressed proteins revealed that these were involved in energy metabolism pathways,protein metabolism,and heat shock.In the present study,the investigators determined the changes in the levels of some proteins,and their expression at the protein and molecular levels in chrysanthemum to help reveal the mechanism of heat resistance in chrysanthemum.Furthermore,the present study elucidated some of the proteins correlated to heat resistance in chrysanthemum,and their expression changes at the protein and molecular levels to help reveal the mechanism of heat resistance in this flower species.These results provide a theoretical basis for the selection of new heat resistant varieties of chrysanthemum in the field. 展开更多
关键词 CHRYSANTHEMUM high temperature stress PROTEOMICS differential protein EXPRESSION
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Attack of Tunisian Phosphate Ore by a Mixture of Sulfuric and Phosphoric Acid: Thermochemical Study by Means of Differential Reaction Calorimetry 被引量:1
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作者 Olfa Lachkar-Zamouri Khemaies Brahim +1 位作者 Feten Bennour-Mrad Ismail Khattech 《Advances in Materials Physics and Chemistry》 2018年第10期411-427,共17页
A calorimetric, Differential Reaction Calorimetry (DRC), study of the thermochemical of the attack of a phosphate ore from Gafsa region (Tunisia) by a mixture of sulfuric and phosphoric acid is undertaken at different... A calorimetric, Differential Reaction Calorimetry (DRC), study of the thermochemical of the attack of a phosphate ore from Gafsa region (Tunisia) by a mixture of sulfuric and phosphoric acid is undertaken at different solid-liquid ratio and different temperature. The plot of the quantity of heat measured by integrating the raw signal as a function of the dissolved mass in the same volume solution at 25℃ presents three straight segments attributed at the formation of the hemihydrate (CaSO4·1/2H2O:HH), the dihydrate (CaSO4·2H2O:DH) or a mixture of these two products checked by X-ray diffraction, infrared spectroscopy and thermal analysis (Differential Scanning Calorimeter: DSC). The attack by the acid mixture was performed at higher temperature and showed in addition the formation of another form of calcium sulfate:anhydrous (CaSO4:AH). Moreover, the variation of mass enthalpy versus temperature presents a break at the T = 45℃. According to our results, it seems that the effect of the temperature on the sulfo-phosphoric attack reaction on the natural phosphate (NP) generates a change of mechanism at around 45℃. 展开更多
关键词 Dissolution THERMOCHEMISTRY differential Reaction CALORIMETER PHOSPHATE ORE Liquid/Solid temperature
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Spatio-Temporal Variability in Land Surface Temperature and Its Relationship with Vegetation Types over Ibadan, South-Western Nigeria 被引量:1
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作者 Blessing Bolarinwa Fabeku Ifeoluwa Adebowale Balogun +1 位作者 Suleiman Abdul-Azeez Adegboyega Orimoloye Ipoola Faleyimu 《Atmospheric and Climate Sciences》 2018年第3期318-336,共19页
Ibadan has experienced a rapid urbanization over the past few decades due to heavy influx of people from different parts of the country as a result of improved economy of the region. This development induced a great c... Ibadan has experienced a rapid urbanization over the past few decades due to heavy influx of people from different parts of the country as a result of improved economy of the region. This development induced a great change in land use and land cover over the region which has become a major environmental concern recently. This study assessed Land Surface Temperature (LST) and its spatio-temporal relationship with land cover type over Ibadan. Land use/Land cover dynamics were assessed using index maps generated from Landsat Satellite data (TM, ETM+ and OLI) of Ibadan. The corrected thermal Infrared bands of the Landsat data were used to retrieve LST. The results revealed a notable increase in built-up areas from 5.64% of the total land cover area in 1984 to 14.05% in 2014. This change has caused increase in surface temperature of Ibadan from 3.56?C to 8.54?C between 1984 and 2014 respectively. The study recorded a continuous decrease in the vegetal part of Ibadan (from 43.28% in 1984 to 14.76 in 2014) which could be attributed to anthropogenic activities as the vegetated land area lost was been converted to other form of land use. The change was found to be positively correlated to the surface temperature intensity over the region with correlation coefficient, r value of 0.9251, 0.8256 and 0.7017 in 1984, 2000 and 2014 respectively. It is recommended that Policies should be considered for planting trees, new guidelines for urban landscape design and construction. 展开更多
关键词 LAND Surface temperature (LST) LAND COVER INDEX Normalized differential VEGETATION INDEX (NDVI)
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ANALYSIS OF STRESS AND TEMPERATURE IN THE CONFORM FORMING PROCESS--FOUNDATION THEORY
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作者 Peng Yuelin Hu Jian Mo Bin 《Journal of Central South University》 SCIE EI CAS 1996年第2期50-55,共6页
The change of stress and temperature in the conform forming process has been studied. On the basis of the law of momentum, the law of momantum moment and the law of energy conservation, the governmental differential e... The change of stress and temperature in the conform forming process has been studied. On the basis of the law of momentum, the law of momantum moment and the law of energy conservation, the governmental differential equations of stress and temperature in the conform metal forming process have been derived, whose definite conditions are given by material mechanics, elastic machanics and plastic mechanics. The analytic solution of these equations has been successfully obtained and as a result, the solid foundations and scientific guide for the further development of this prospective metal processing techique have been established. 展开更多
关键词 CONFORM stress temperature differential equations
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CUTTING TEMPERATURE OF CBN TOOLS WHEN MACHINING STEEL OF MEDIUM HARDNESS
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作者 陈五一 韩书文 《Chinese Journal of Aeronautics》 SCIE EI CSCD 1998年第1期67-70,共4页
CUTTINGTEMPERATUREOFCBNTOOLSWHENMACHININGSTEELOFMEDIUMHARDNESSChenWuyi1(陈五一),DavidK.Aspinwal2,HanShuwen3(韩书文... CUTTINGTEMPERATUREOFCBNTOOLSWHENMACHININGSTEELOFMEDIUMHARDNESSChenWuyi1(陈五一),DavidK.Aspinwal2,HanShuwen3(韩书文)1BeijingUniversi... 展开更多
关键词 CBN cutting regime temperature partial differentiation
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Sex determination and dif ferentiation in Aurelia sp.1: the absence of temperature dependence
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作者 刘春胜 顾志峰 +3 位作者 邢孟欣 孙云 陈四清 陈昭廷 《Journal of Oceanology and Limnology》 SCIE CAS CSCD 2018年第2期457-464,共8页
Cnidarians, being regarded as ‘basal' metazoan animals, are considered to have relatively high plasticity in terms of sex reversal. In this study we used an experimental approach to demonstrate sexual diff erenti... Cnidarians, being regarded as ‘basal' metazoan animals, are considered to have relatively high plasticity in terms of sex reversal. In this study we used an experimental approach to demonstrate sexual diff erentiation and plasticity in benthic polyps and pelagic medusae of A urelia sp.1 maintained at dif ferent temperatures. Results indicated that in A urelia sp.1, sex diff erentiation has been determined at the polyp stage and that all medusae originating from a given polyp are, phenotypically, of the same sex. In addition, the sex of polyps budding from the same clone(either male or female) at dif ferent temperatures appears to be the same as that of the parent. The sex of medusae that had originated from a known-sex polyp was observed to remain the same as that of the parent, irrespective of differences in strobilation or rearing temperatures. These results indicate that the mechanism of sex determination of Aurelia sp.1. is not influenced by prevailing temperature regimes. A comparison of variability in terms of sexual plasticity of A urelia sp.1 with that of Hydrozoa and Anthozoa suggests that species characterized by a free-swimming medusa life stage have a high dispersal potential, which probably results in a lower rate of sex reversal. 展开更多
关键词 A urelia sp.1 sex determination temperature sex differentiation
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Evaluation of negative bias temperature instability in ultra-thin gate oxide pMOSFETs using a new on-line PDO method
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作者 纪志罡 许铭真 谭长华 《Chinese Physics B》 SCIE EI CAS CSCD 2006年第10期2431-2438,共8页
A new on-line methodology is used to characterize the negative bias temperature instability (NBTI) without inherent recovery. Saturation drain voltage shift and mobility shift are extracted by ID-VD characterization... A new on-line methodology is used to characterize the negative bias temperature instability (NBTI) without inherent recovery. Saturation drain voltage shift and mobility shift are extracted by ID-VD characterizations, which were measured before stress, and after every certain stress phase, using the proportional differential operator (PDO) method. The new on-line methodology avoids the mobility linearity assumption as compared with the previous onthe-fly method. It is found that both reaction-diffusion and charge-injection processes are important in NBTI effect under either DC or AC stress. A similar activation energy, 0.15 eV, occurred in both DC and AC NBTI processes. Also degradation rate factor is independent of temperature below 90℃ and sharply increases above it. The frequency dependence of NBTI degradation shows that NBTI degradation is independent of frequencies. The carrier tunnelling and reaction-diffusion mechanisms exist simultaneously in NBTI degradation of sub-micron pMOSFETs, and the carrier tunnelling dominates the earlier NBTI stage and the reaction-diffusion mechanism follows when the generation rate of traps caused by carrier tunnelling reaches its maximum. 展开更多
关键词 negative bias temperature instability proportional differential operator DEGRADATION
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Effects of C60 on the Glass Transition Temperature of Carbazole-based Photorefractive Polyphosphazenes
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作者 陈百利 CHEN Shufan +5 位作者 LUO Xuan FANG Yu ZHANG Qingjun HUANG Chuanqun DENG Qinghua 吴卫东 《Journal of Wuhan University of Technology(Materials Science)》 SCIE EI CAS 2018年第4期974-979,共6页
The bi-functional carbazole-based photorefractive polyphosphazenes with different content of C_(60)-doped were fabricated. The glass transition temperature(T_g) of these polymer composite materials was determined ... The bi-functional carbazole-based photorefractive polyphosphazenes with different content of C_(60)-doped were fabricated. The glass transition temperature(T_g) of these polymer composite materials was determined using a differential scanning calorimetric(DSC) method. According to the DSC measurement results with different heating rates, the variation of T_g and the active energy of glass transition(E_g) were analyzed in detail. The analysis results indicate that the transition region shifts to higher temperatures with increasing heating rate, and C_(60) content(below 1.0 wt%) can influence the T_g of photorefractive polyphosphazenes. The T_g first increases and then decreases with the C_(60) content(below 1.0 wt%). The probable causes of the influence of C_(60) on T_g was proposed. 展开更多
关键词 differential scanning calorimetric (DSC) fullerene C60 carbazole-based photorefractivepolyphosphazenes glass transition temperature (Tg) active energy of glass transition (Eg)
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Transient thermal behavior of radial fins of rectangular,triangular and hyperbolic profiles with temperature-dependent properties using DTM-FDM 被引量:4
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作者 Sobhan Mosayebidorcheh Mohammad Rahimi-Gorji +3 位作者 D.D Ganji Taha Moayebidorcheh O Pourmehran M.Biglarian 《Journal of Central South University》 SCIE EI CAS CSCD 2017年第3期675-682,共8页
This work focuses on transient thermal behavior of radial fins of rectangular,triangular and hyperbolic profiles with temperature-dependent properties.A hybrid numerical algorithm which combines differential transform... This work focuses on transient thermal behavior of radial fins of rectangular,triangular and hyperbolic profiles with temperature-dependent properties.A hybrid numerical algorithm which combines differential transformation(DTM) and finite difference(FDM) methods is utilized to theoretically study the present problem.DTM and FDM are applied to the time and space domains of the problem,respectively.The accuracy of this method solution is checked against the numerical solution.Then,the effects of some applicable parameters were studied comparatively.Since a broad range of governing parameters are investigated,the results could be useful in a number of industrial and engineering applications. 展开更多
关键词 特性曲线 温度依赖 热行为 散热片 三角形 瞬态 矩形 双曲线
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Simulation of Thermal Explosion of Catalytic Granule in Fluctuating Temperature Field
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作者 Igor Derevich Daria Galdina 《Journal of Applied Mathematics and Physics》 2013年第5期1-7,共7页
Method for numerical simulation of the temperature of granule with internal heat release in a medium with random temperature fluctuations is proposed. The method utilized the solution of a system of ordinary stochasti... Method for numerical simulation of the temperature of granule with internal heat release in a medium with random temperature fluctuations is proposed. The method utilized the solution of a system of ordinary stochastic differential equations describing temperature fluctuations of the surrounding and granule. Autocorrelation function of temperature fluctuations has a finite decay time. The suggested method is verified by the comparison with exact analytical results. Random temperature behavior of granule with internal heat release qualitatively differs from the results obtained in the deterministic approach. Mean first passage time of granules temperature intersecting critical temperature is estimated at different regime parameters. 展开更多
关键词 Stochastic Ordinary differential Equation AUTOCORRELATION Function Heat Explosion Semenov’s DIAGRAM temperature FLUCTUATIONS
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Determination of the liquidus and solidus temperatures of FeCrAl stainless steel
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作者 Zhi-biao Han Jian-hua Liu +3 位作者 Yang He Kang-wei Li Yi-long Ji Jian Liu 《International Journal of Minerals,Metallurgy and Materials》 SCIE EI CAS CSCD 2015年第11期1141-1148,共8页
The liquidus and solidus temperatures of FeCrAl stainless steel were determined by differential scanning calorimetry(DSC) at different heating rates. They were also calculated by Thermo-calc software and empirical f... The liquidus and solidus temperatures of FeCrAl stainless steel were determined by differential scanning calorimetry(DSC) at different heating rates. They were also calculated by Thermo-calc software and empirical formulae separately. The accuracy of calculation results was assessed by comparison with the corresponding DSC results. The liquidus temperatures calculated by empirical formulae, which exhibited a maximum deviation of 8.6℃ were more accurate than those calculated using Thermo-calc, which exhibited a maximum deviation of 12.11℃. On the basis of Thermo-calc calculations performed under the Scheil model, the solidus temperature could be well determined from solid fraction(fS) vs. temperature(t) curves at fS = 0.99. Furthermore, a theoretical analysis to determine the solidus temperature with this method was also provided. 展开更多
关键词 ferritic stainless steel liquidus temperature solidus temperature differential scanning calorimetry
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New Neumerical Method to Calculate Time-Dependent Quantum Properties in Finite Temperature Based on the Heisenberg Equation of Motion
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作者 Shin-Ichiro Kondo 《Journal of Modern Physics》 2012年第10期1537-1549,共13页
For the purpose of computer calculation to evaluate time-dependent quantum properties in finite temperature, we propose new numerical method expressed in the forms of simultaneous differential equations. At first we d... For the purpose of computer calculation to evaluate time-dependent quantum properties in finite temperature, we propose new numerical method expressed in the forms of simultaneous differential equations. At first we derive the equation of motion in finite temperature, which is found to be same expression as Heisenberg equation of motion except for the c-number. Based on this equation, we construct numerical method to estimate time-dependent physical properties in finite temperature precisely without using analytical procedures such as Keldysh formalism. Since our approach is so simple and is based on the simultaneous differential equations including no terms related to self-energies, computer programming can be easily performed. It is possible to estimate exact time-dependent physical properties, providing that Hamiltonian of the system is taken to be a one-electron picture. Furthermore, we refer to the application to the many body problem and it is numerically possible to calculate physical properties using Hartree Fock approximation. Our numerical method can be applied to the case even when perturbative Hamiltonians are newly introduced or Hamiltonian shows complex time-dependent behavior. In this article, at first, we derive the equation of motion in finite temperature. Secondly, for the purpose of verification and of exhibiting the usefulness, we show the derivation of gap equation of superconductivity and of sum rule of electrical conductivity and the application to the many body problem. Finally we apply this method to these two cases: the first case is most simplified resonance charge transfer neutralization of an ion and the second is the same process but impurity potential is newly introduced as perturbative Hamiltonian. Through both cases, it is found that neutralization process is not so sensitive to temperature, however, impurity potential as small as 10 meV strongly influences the neutralization of ion. 展开更多
关键词 HEISENBERG EQUATION of Motion NEUMANN EQUATION TIME-DEPENDENT Physical Properties Finite temperature Numerical Solutions Simultaneous differential EQUATIONS
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