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Universal scaling of latent heat of orbital order-disorder transition with average R-site i

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Universal scaling of latent heat of orbital order-disorder transition with average R-site ion size in perovskite RMnO3 systemsParthasarathi Mondal and Dipten Bhattacharya*Electroceramics Division, Central Glass and Ceramic Research Institute, Calcutta 700 032, IndiaThe latent heat (L) of orbital order-disorder transition in single-valent perovskite manganite series La1-xRxMnO3 (R = Pr, Nd, Gd; x = 0.0-1.0) decreases with the decrease in average R-site radius <rR> following a universal scaling law L.<rR>2/σ2 ~ exp(<rR>), where σ2 is the variance in R-site radius, and eventually reaches zero at a critical R-site radius <rR>c ≈ 1.180 Å. Such a drop in L is due, possibly, to a universal pattern of evolution of finer orbital domain structure with the drop in <rR> as well as with the increase in σ2 irrespective of R-site ion type.PACS Nos. 71.70.Ej, 1Differentorbitalphaseshavebeenidentifiedboththeoreticallyandexperimentally in a series of strongly correlated electron systems.1 They range from orbital solid, liquid, glass, liquid crystal to more esoteric phases in two-dimensional triangular lattice (LiVO2) or one dimensional TiOCl, charge transfer insulators, or spinels with transition metal ions having partially filled t2g levels at B-sites as in NaTiO2 (orbitally induced Peierls phase) etc.2-6 The study of evolution of one phase to another is quite fascinating and rewarding as it provides insights into the fine interplay among orbital, spin, charge, and lattice degrees of freedom. It also offers clues for newer microelectronic applications based on orbitronics.7 One of the techniques commonly employed in characterizing an orbital phase and its evolution is the study of its phase transition characteristics. Recent results8-12 in this regard provide very interesting picture. The first order transition, characterized by finite latent heat and lattice volume contraction, gives way to second order transition as lattice distortion increases. More direct characterization of the orbital phases using local structural data provides information about the orbital domain size and its temporal fluctuations. As lattice distortion increases, the orbital domains undergo spatio-temporal evolution with decrease in size and increase in temporal fluctuation. This, in turn, leads to evolution in the order of the transition. For few selected undoped and doped perovskite manganite compounds like LaMnO3, La0.8Ca0.2MnO3, Pr0.6Ca0.4MnO3, the orbital domain size has been estimated.13,14 However, there is, as yet, no systematic mapping of spatio-temporal fluctuation of the orbital domains available across the entire phase diagram of strongly correlated electron system as a function of evolution of phase transition order. Neither is there any systematic mapping of the evolution of the phase transition as a function of lattice2distortion. In this paper, we attempt to provide, at least, a mapping of variation of latent heat (L) associated with the orbital order-disorder transition as a function of average Rsite ion radius (<rR>) in a series of undoped perovskite RMnO3.We report that L decreases with the decrease in <rR> and reaches zero at a critical <rR>c ≈ 1.180 Å. We also report that L depends on variance σ2 as well, especially, around the zone where σ2 → σ2max. It is possible to show that the modified L.<rR>2/σ2 exhibits a universal scaling with <rR>.The experiments have been carried out on high quality bulk polycrystalline samples. They are prepared by compacting the powder, obtained through solution chemistry route11 and subsequent calcination and sintering under inert (Ar) atmosphere at 1300-1400oC for 5-10 h. The samples have been characterized by X-ray diffraction (XRD), energy dispersive X-ray (EDX), scanning electron microscopy (SEM), chemical analysis for estimation of Mn4+ concentration, dc resistivity measurements etc. The calorimetric measurements have been carried out in differential thermal analyzer (DTA) of Shimadzu, Japan and in differential scanning calorimeter (DSC) of Perkin-Elmer (Pyris Diamond DSC). The dc resistivity has been measured over a temperature regime 300-1200 K using high quality platinum paste and wires. The contacts were cured overnight at 1400 K under inert atmosphere.The Mn4+ concentration is found to vary within 2-4% in all the cases. The estimation of room temperature lattice parameters, orthorhombic distortion (D), and3volume (V) reveals systematic patterns of variation with the decrease in <rR> (Fig. 1). It is interesting to note that, at room temperature, both V and D of different systems follow a rather universal pattern of variation with <rR> with a small scattering due to difference in R-site ion type – La, Pr, Nd, Gd. For comparison, the patterns of variation of V and D with the doping level (x) are shown in Fig. 1. The V, D versus x pattern depends clearly on the R-site ion type.In Fig. 2, we show the resistivity vs. temperature plots, and the DTA/DSC thermograms. The transition temperatures (TJT), obtained from these studies, corroborate each other and confirm the consistency in the quality of the samples. The latent heat (L) is calculated from the DSC thermograms by properly subtracting the background. In Fig. 2c, L is shown as a function of x for all the ions – Pr, Nd, and Gd – while the TJT versus x patterns are shown in Fig. 2d. L is found to drop with x following different patterns depending on the type of ion: (i) for Pr, it drops sharply within x = 0.0-0.2, then a rather flat pattern over x = 0.2-0.7, and finally a sharp drop for x = 0.7-1.0; (ii) for Nd, it drops sharply within x = 0.0-0.3 and then gradually over x = 0.3-0.7; (iii) for Gd, it drops sharply to zero within x = 0.0-0.33. TJT, as expected, rises linearly with x for each series with ion dependent slope dTJT/dx: ~33 for Pr, ~40 for Nd, and ~39 for Gd. The reason behind different patterns of drop in L with x for different ions could be the doping induced disorder σ2, which varies from ion to ion. The slight decrease in dTJT/dx for Gddoped samples could be due to marginally higher Mn4+ content in those samples. In Fig. 3, we show that suitable choice of the scaling parameters helps in collapsing the set of L versus x patterns. The plot of L.<rR>2/σ2 versus <rR> depicts a universal pattern.4Therefore, it appears that irrespective of the R-site ion type the crossover from first to higher order transition of the orbital phase depends only on <rR> and σ2. This is the central result of this work.It is clear from the entire set of crystallographic and calorimetric measurements that the doping induced disorder due to mismatch in R-site ion size does influence the latent heat (L) although it fails to influence the global structural parameters such as lattice volume (V) or orthorhombic distortion (D). The role of σ2 is subtle. We can rationalize these observations by resorting to a concept of variation in orbital domain size depending on overall lattice distortion due both to <rR> and σ2. The orbital domain sizes have been estimated13,14 for LaMnO3, La0.8Ca0.2MnO3, and Pr0.6Ca0.4MnO3 systems and are found to be varying between 4000-400 Å with the decrease in domain size in the case of doped systems as well as for systems with smaller R-site radius. These data give an idea that the orbital domain size does decrease as doping level increases and/or <rR> decreases. The evolution of L to zero at <rR>c shows that irrespective of ion type at R-site, orbital domain size in such cases reaches a certain universal value that offers L comparable to or below the instrument resolution in global calorimetry. Only a high precision local calorimetry might resolve the latent heat of transition in such cases.15 The increase in disorder too leads to decrease in orbital domain size due, possibly, to segregation of structurally dissimilar phases. It turns out that L is more sensitive to the variation in orbital domain size than the global crystallographic parameters V and D.5The interplay of Jahn-Teller orbital order with GdFeO3-type tilt order in RMnO3 has earlier been shown16 to give rise to d-type orbital order for those cases where tilt is large due to smaller <rR>. This results from covalency in R-O bonds. In a recent model17 it has been shown how elastic near-neighbor and next-near-neighbor interaction among the Jahn-Teller ions and/or impurities stabilizes different superstructures including orbital domains. The strain field (E) due to impurities or Jahn-Teller ions has long-range (r) effect as E ~ 1/r3 [Ref. 18]. As a result, coupling of defects and/or Jahn-Teller ions develop for formation of different orbital order superstructures. In this scenario, it is possible to envisage a model of interference of strain fields originating from different sources: (i) Jahn-Teller ions, (ii) R-site mismatch which, in turn, gives rise to tilt in Mn3+O6 octahedra, and (iii) phase segregation due to large σ2. Such interference will limit the growth of orbital order and will give rise to orbital domains. Finally, the domain boundary energy will determine the orbital domain size. Since L depends directly on the orbital domain size, universal pattern of drop in L with <rR> and σ2 signifies that the orbital domain size also decreases following a universal pattern. The interesting point here is that since such orbital domain structure does not depend on R-site ion type, it is possible to design an orbital domain structure by R-site ion type invariant choice of <rR> and σ2. This will certainly bring more flexibility in designing a domain structure for orbitronics-based applications. The quantitative estimation of universal evolution pattern of orbital domain structure as a function of <rR> and σ2 will be attempted in future.In summary, we report a rather universal pattern of variation in latent heat of orbital order-disorder transition in perovskite RMnO3 series with the average R-site ion6size. It has been found that irrespective of R-site ion type the latent heat becomes zero at a critical R-site size <rR>c ~ 1.180 Å. The role of doping induced disorder on the latent heat is palpable, especially, where it attains maximum. Such a pattern could possibly be due to a universal pattern of evolution of orbital domain structure as a function of both <rR> and σ2. Our observation creates a possibility of tuning the orbital order melting with desired latent heat at a desired temperature through subtle engineering with <rR> and σ2 and thus can be utilized in applications based on orbitronics.7*Electronic mail: dipten@cgcri.res.in1Y. Tokura and N. Nagaosa, Science 280, 462 (2000); J. van den Brink, G. Khaliullin,and D.I. Khomskii, in Colossal Magnetoresistive Manganites, edited by T. Chatterji (Kluwer, Dordrecht, 2002); D.I. Khomskii, Phys. Scr. 72, CC8 (2005); T. Hotta, condmat/0604467 (2006).2H.F. Pan, J. van den Brink, D.I. Khomskii, and G.A. Sawtzky, Phys. Rev. Lett. 78, 1323(1997).3V. Kataev, J. Baier, A. Moeller, L. Jongen, G. Meyer, and A. Freimuth, Phys. Rev. B 68,140405 (R) (2005).4Y. Motome and H. Tsunetsugu, J. Phys. Soc. Jpn. 74, suppl. 208 (2005).5D.I. Khomskii and T. Mizokawa, Phys. Rev. Lett. 94, 156402 (2005).6M.V. Mostovoy and D.I. Khomskii, Phys. Rev. Lett. 92, 167201 (2004).7See, for example, Y. Tokura, Phys. Today 56(7), 50 (2003).8J.-S. Zhou and J.B. Goodenough, Phys. Rev. B 68, 144406 (2003).9T. Chatterji, F. Fauth, B. Ouladdiaf, P. Mandal, and B. Ghosh, Phys. Rev. B 68, 052406(2003).10T. Chatterji, B. Ouladdiaf, P. Mandal, and B. Ghosh, Solid State Commun. 131, 75(2004).11D. Bhattacharya, P.S. Devi, and H.S. Maiti, Phys. Rev. B 70, 184415 (2004).12N. Das, P. Mondal, and D. Bhattacharya, Phys. Rev. B 74, 014410 (2006).813C. S. Nelson, J. P. Hill, D. Gibbs, F. Yakhou, F. Livet, Y. Tomioka, T. Kimura, and Y.Tokura, Phys. Rev. B 66, 134412 (2002).14G. Papavassiliou, M. Belesi, M. Fardis, M. Pissas, J. Dolinsek, C. Dimitropoulose, andJ.P. Ansermet, Phys. Rev. Lett. 91, 147205 (2005).15See, for example, A. Soibel, E. Zeldov, M. Rappaport, Y. Maesoedov, T. Tamegai, S.Ooi, M. Konczykowski, and V.B. Geshkenbein, Nature (London) 406, 282 (2000).16T. Mizokawa, D.I. Khomskii, and G.A. Sawatzy, Phys. Rev. B 60, 7309 (1999).17See, for example, D.I. Khomskii and K.I. Kugel, Phys. Rev. B 67, 134401 (2003);S.J.L. Billinge and P.M. Duxbury, Phys. Rev. B 66, 064529 (2002).18J.D. Eshelby, The continuum theory of lattice defects in Solid State Physics, edited by F.Seitz and D. Turnbull (Academic, New York, 1956) vol. 3, p. 79.9245 244 243La1-xPrxMnO3 La1-xGdxMnO3 La1-xNdxMnO34.0245 2444.03.5243 Lattice Volume (Å3 ) 2423.5Lattice Volume (Å3)242 3.0D (%)240 239 238 237 236 0.0 0.2 0.4 2.0 2.5240 239 238 237 2.0 2.5(a)0.6 0.8 1.0236(b)1.5 <rR> (Å)1.22 1.21 1.20 1.19 1.18 1.17 1.16xFig. 1. Room temperature structural data for La1-xPrxMnO3, La1-xNdxMnO3, and La1-xGdxMnO3: (a) the lattice volume (solid symbols) and orthorhombic distortion (open symbols) as a function of x and (b) the lattice volume and orthorhombic distortion as a function of <rR>.10D (%)2412413.0Fig. 2.(color online). The typical dc resistivity versus temperature plots (a) and the DSCand DTA thermograms (b) for few representative samples; (c) the latent heat versus x patterns for all the three series La 1-x R x MnO 3 (R = Pr, Nd, Gd) and (d) the corresponding T JT versus a plots.60070080090010001100-101234567H e a t I n p u t (m W )T (K)-20-15-10-501: LaMnO 32: La 0.95Gd 0.05MnO 33: La 0.9Gd 0.1MnO 34: La 0.8Pr 0.2MnO 35: La 0.7Pr 0.3MnO 36: La 0.5Pr 0.5MnO 37: La 0.3Pr 0.7MnO 38: La 0.1Pr 0.9MnO 38766554433211(b)D T A (μV )6007008009001000110010-210-11001: LaMnO 32: La 0.9Gd 0.1MnO 33: La 0.8Pr 0.2MnO 34: La 0.7Pr 0.3MnO 35: La 0.5Pr 0.5MnO 354321(a) T (K)R e s i s t i v i t y (Ω-c m )510152025 xL a t e n t H e a t (J o u l e /g )700800900100011001200T J T (K )xFig. 3. The universal scaling of L.<r R >2/σ2 with <r R >: L.<r R >2/σ2 ~A.exp[B.<r R >], A =e -95.6 and B = 78.2; inset shows the latent heat versus <r R > plot for all the three series of compounds.10-310-210-1ÅL .<r A >2/σ2<r A > ( )。

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气象常用专业英语词汇

气象常用专业英语词汇

气象常用专业英语词汇pressure gradient 气压梯度 barometric height formula 压高公式 pressure gradient force 气压梯度力 Coriolis force 科里奥利力 water vapor 水［蒸］汽 water vapor pressure 水汽压 humidity 湿度 relative humidity 相对湿度 absolute humidity 绝对湿度 specific humidity 比湿 mixing ratio 混合比dew point ［temperature ］露点（温度） depression of the dew point （温度）露点差 super-saturated air 过饱和空气 saturation specific humidity 饱和比湿 saturation vapor pressure 饱和水汽压 saturation deficit 饱和差 cloud 云low cloud 低云 middle cloud 中云 highcloud 高云 cloud amount 云量 cloud height 云高 cloud genera 云属 cloud etage 云族 cloud species 云种 cloud variety 云类 cloud form 云状 cirrus, Ci 卷云 cirrostratus, Cs 卷层云 cirrocumulus, Cc 卷积云altocumulus, Ac 高积云 altostratus, As 高层云 cumulus, Cu 积云cumulus humilis, Cu hum 淡积云 cumulus congestus, Cucon 浓积云 cumulonimbus, Cb 积雨云 cumulus fractus, Cu fra 碎积云stratocumulus, Sc 层积云 stratus, St 层云 nimbostratus, Ns 雨层云 stratiform cloud 层状云 cumuliform cloud 积状云 cold cloud 冷云 warm cloud 暖云 ice cloud 冰云1 / 10主题词表English Chinese 01.大气atmospheric science 大气科学 meteorology 气象学 atmosphere 大气atmospheric impurity 大气杂质atmospheric suspended matter 大气悬浮物 atmospheric composition 大气成分 atmospheric mass 大气质量 atmospheric density 大气密度 atmospheric subdivision 大气分层 homosphere 均质层 heterosphere 非均质层standard ［pressure ］ level 标准层 isothermal layer 等温层 lower atmosphere 低层大气 middle atmosphere 中层大气 upper atmosphere 高层大气 troposphere 对流层 tropopause 对流层顶 stratosphere 平流层 stratopause 平流层顶 mesopause 中间层顶 thermosphere 热层 exosphere 夕卜［逸］层 ionosphere 电离层 magnetosphere 磁层 ozonosphere 臭氧层 free atmosphere 自 由大气 planetary atmosphere 行星大气standard atmosphere （reference atmosphere ）标准大气（参考homogeneous atmosphere 均质大气 isothermal atmosphere 等温大气polytropic atmosphere 多元大气 scale height 大气标高 meteorological element 气象要素 air temperature 气温 wet-bulb temperature 湿球温度 dry-bulb temperature 干球温度 atmospheric pressure 气压standard atmosphere pressure 标准大气压 station pressure 本站气压 sea-level pressure 海平面气压气象常用专业英语词汇precipitation intensity 降水强度 showery precipitation 阵性降水 convective precipitation 对流性降水 orographic precipitation 地形降水 rain 雨 rain drop 雨滴 rain shadow 雨影 glaze 雨淞 rain day 雨日rainfall ［amount ］雨量continuous precipitation 连续性降水 intermittent precipitation 间歇性降水 showery rain 阵雨freezing rain 冻雨 drizzle 毛毛雨 light rain 小雨moderate rain 中雨 heavy rain 大雨 torrential rain 暴雨 local precipitation 地方性降水 orographic rain 地形雨 storm 风暴sandstorm, duststorm 沙［尘］暴 hail storm 雹暴 haze 霾 dust 浮尘 dew 露 frost 霜 frost point 霜点 first frost 初霜 latest frost 终霜 tornado 龙卷 dust devil 尘卷风 snow 雪 sleet 雨夹雪showery snow 阵雪 snow crystal 雪晶 snowflake 雪花 snow grains 米雪 snowstorm 雪暴 snow cover 积雪 snowfall ［amount ］雪量 snow depth 雪深 snow day 雪日 icing 积冰 hail 冰雹 2 / 10wind 风wind direction 风向wind speed, wind velocity 风速 maximum wind speed 最大风速 extreme wind speed 极大风速 wind speed profile 风速廓线 wind force 风力wind force scale 风级Beaufort ［wind ］ scale 蒲福风级 calm 0级风 light air 1 级风 light breeze 2 级风 gentle breeze 3 级风 moderate breeze 4 级风 fresh breeze 5 级风 strong breeze 6 级风 near gale 7 级风 gale 8级风 strong gale 9 级风 storm 10 级风 violent storm 11 级风 hurricane 12 级风gust 阵风local wind 地方性风 surface wind 地面风 foehn 焚风mountain-valley breeze 山谷风 sea-land breeze 海陆风 on-shore wind 向岸风 off-shore wind 离岸风 gorge wind 峡谷风predominant wind direction 主导风向 prevailing wind 盛行风 wind pressure 风压 wind energy 风能wind energy resources 风能资源 wind energy rose 风能玫瑰［图］ visibility 能见度 clear sky 晴天 partly cloudy 少云 cloudy 多云 overcast 阴天blue of the sky 天空蓝度 skycondition 天空状况 precipitation 降thermometer 温度表 telethermometer 遥测温度表 thermograph 温度计 geothermometer 地温表 surface geothermometer 地面温度表 angle geothermometer 曲管地温表 tube-typed geothermometer 直管地温表 maximum thermometer 最高温度表 minimumthermometer 最低温度表 mercury thermometer 水银温度表 Lyman- a hygrometer 莱曼-a 湿度表 bimetallic thermograph 双金属片温度计 barograph 气压计 aneroid barograph 空盒气压计 mountain barograph 高山气压计 barometer 气压表 aneroid barometer 空盒气压表 ship-barometer 船用气压表 mountain barometer 高山气压表 pressure altimeter 气压测高表 normal barometer 标准气压表 mercury barometer 水银气压表 Fortin barometer 福丁气压表 Kew pattern barometer 寇乌气压表hygrograph 湿度计 hygrometer 湿度表 psychrometer 干湿表 aspirated psychrometer 通风干湿表 Assmann psychrometer 阿斯曼干湿表 dew-point hygrometer 露点湿度表 hair hygrometer 毛发湿度表 hair hygrograph 毛发湿度计black and white bulb thermometer 黑白球温度表barothermograph 气压温度计 dry-bulb thermometer 干球温度表 wet-bulb thermometer 湿球温度表 sunshine recorder 日照计Jordan sunshine recorder 乔唐日照计Campbell-Stokes sunshine recorder 康培尔-司托克日照计 pyrheliometer 直接辐射表 pyranometer 总辐射表 sky radiometer diffusometer 天空辐射表 albedometer 反照率表 pyranometer 净辐射表 evaporograph 蒸发计 evaporation pan 小型蒸发器3 / 10thunder 雷 thunderstorm 雷暴 thunder shower 雷阵雨 lightning 闪电 fog 雾 mist 轻雾 wet fog 湿雾 sea fog 海雾 ice fog 冰雾 frontal fog 锋面雾 advection fog 平流雾 radiation fog 辐射雾advection-radiation fog 平流辐射雾 mixing fog 混合雾 evaporation fog 蒸发雾 supercooled fog 过冷却雾 ground fog 地面雾 upslope fog 上坡雾 air-mass fog 气团雾 tropical air fog 热带气团雾 rime 雾淞graupel 霰percentage of sunshine 日照百分率 sunshine duration 日照时数duration of possible sunshine 可照时数 02.大气探测atmospheric sounding and observing 大气探测 meteorological observation 气象观测 surface observation 地面观测 visual observation 目测background pollution observation 本底污染观测 field observation 外场观测 conventional observation 常规观测 sounding 探空upper air observation 高空观测 aircraft sounding 飞机探测 rocket sounding 火箭探测 radio sounding 无线电探空 surface data 地面资料 upper air data 高空资料 observation site 观测场coagulation 碰并 ice crystal 冰晶 ice point 冰点 condensation 凝结 evaporation 蒸发 solidification 凝固 deposition 凝华 sublimation 升华freezing 冻结condensation nucleus 凝结核 salt nucleus 盐核weather modification 人工影响天气 cloud dissipation ^肖云 salt-seeding 盐粉播撒 frost prevention 防霜artificial precipitation 人工降水 cloud cluster 云团tropical cloud cluster 热带云团 cloud system 云系comma cloud system 逗点云系 banded cloud system 带状云系 vortex cloud system 涡旋云系 atmospheric radiation 大气辐射 solar radiation 太阳辐射solar constant 太阳常数outgoing long-wave radiation, OLR 向外长波辐射 visible light 可见光 radiation balance 辐射平衡 global radiation 总辐射 direct radiation 直接辐射 effective radiation 有效辐射 scattered radiation 散射辐射 diffuse radiation 漫射辐射sky radiation 天空辐射upward ［tatal ］ radiation 向上［全］辐射 downward ［total ］ radiation 向下［全］辐射 incoming radiation 入射辐射albedo of the earth-atmosphere system 地气系统反照率 albedo of underlying surface 下垫面反照率 atmospheric counter radiation 大气逆辐射 radiance 辐射率 albedo 反照率planetary temperature 行星温度 atmospheric window 大气窗［atmospheric ］ absorptivity ［大气］吸收率 primaryevaporation tank 大型蒸发器 standard pan 标准蒸发器 ceiling projector 云幕灯 visibility meter,visiometer 能见度表 raingauge 雨量器 pluviograph,recording raingauge 雨量计 accumulative raingauge 累计雨量器 tilting bucket raingauge 翻斗［式］雨量计 electric conductivity raingauge 水导［式］雨量计 siphon rainfall recorder 虹吸［式］雨量计 rainfall intensity recorder 雨强计 telemetering pluviograph 遥测雨量计 wind vane 风向标 anemometer 风速表contact anemometer 电接风速表 cup anemometer 转杯风速表 propeller anemometer 螺旋桨［式］风速表anemorumbometer 风向风速表 anemograph 风速计 meteorological rocket 气象火箭 sounding rocket 探空火箭 weather radar 天气雷达 meteorological radar 气象雷达 lidar 激光雷达sodar, acoustic radar 声［雷］达 Doppler radar 多普勒天气雷达 atmospheric remote sensing 大气遥感 meteorological satellite 气象卫星 synoptic data 天气资料 real time data 实时资料radiation transfer equation 辐射传输方程atmospheric transmission model 大气传输模式 03.大气物理学atmospheric physics 大气物理［学］ cloud physics 云物理学 advection 平流 convection 对流 aerosol 气溶胶cloud droplet-size distribution 云滴谱 raindrop size distribution 雨滴谱 fog-drop 雾滴 cloud droplet 云滴supercooled cloud droplet 过冷云滴 drop spectrum 滴谱 collision 碰撞scattering 一次散射4 / 10Mie scattering 米散射 smog aerosol 烟雾气溶胶 multiple scattering 多次散射 ash cloud 烟灰云 Rayleigh scattering 瑞利散射smog 烟雾 sky brightness, sky luminance 天空亮度smoke screen 烟幕atmospheric optical thickness, atmospheric optical depth 大 acid rain 酸雨 气光学厚度 smoke 烟 smoke plume 烟羽 plume rise 烟羽抬升 fallout 沉降物05.动力气象学dynamic meteorology 动力气象学 atmospheric thermodynamics 大气热力学 sensible heat 感热 latent heat 潜热reversible adiabatic process 可逆绝热过程 irreversible adiabatic process 不可逆绝热过程 moisture inversion 逆湿thermodynamic equation 热力学方程 temperature inversion 逆温turbulence inversion 湍流逆温 surface inversion 地面逆温 radiation inversion 辐射逆温 capping inversion 覆盖逆温 subsidence inversion 下沉逆温 frontal inversion 锋面逆温 inversion layer 逆温层 temperature gradient 温度梯度 temperature advection 温度平流 adiabatic ascending 绝热上升 adiabatic sinking 绝热下沉 adiabatic cooling 绝热冷却 adiabatic heating 绝热增温 pseudo-adiabatic process 假绝热过程 diabatic process 非绝热过程convective condensation level, CCL 对流凝结高度 mixing condensation level 混合凝结高度 temperature lapse rate 气温直减率dry adiabatic lapse rate 干绝热直减率 moist adiabatic lapse rate 湿绝热直减率 condensation level, CL 凝结高度virtual temperature 虚温dry adiabatic process 干绝热过程 moist adiabatic process 湿绝热过程potential temperature 位温 equation of motion 运动方程 5 / 10［atmospheric］ transparency ［大气］透明度 atmospheric optical phenomena 大气光学现象 atmospheric turbidity 大气浑浊度 mirage 蜃景 twilight 曙暮光 aurora australis 南极光 aurora borealis 北极光 halo 晕 46° halo 46 度晕22° halo 22 度晕 solar halo 日晕 lunar halo 月晕 solar corona 日华 lunar corona 月华 rainbow 虹 secondary rainbow 霓 corona 华 twilight colors 霞 aurora 极光 glory 宝光［环］ magnetic storm 磁暴 04.大气化学atmospheric chemistry 大气化学 atmospheric photolysis 大气光解作用 atmospheric ozone 大气臭氧 atmospheric trace gas 大气痕量气体 photochemical reaction 光化反应photochemical smog 光化烟雾 precipitation chemistry 降水化学 atmospheric background 大气本底［值］ atmospheric pollution 大气污染 air pollution 空气污染 primary pollutant 原生污染物 secondary pollutant 次生污染物 atmospheric cleaning 大气净化 floating dust 飘尘 dustfall 降尘greenhouse gasses 温室气体 atmospheric pollutant 大气污染物southern branch jet stream 南支急流 basic flow 基本气流 subtropical jet stream 副热带急流 axis of jet stream 急流轴 warm advection 暖平流 cold advection 冷平流 upward flow 上升气流 downward flow 下沉气流 geostrophic motion 地转运动 quasi-geostrophic motion 准地转运动 Ekman layer 埃克曼层 Ekman spiral 埃克曼螺线 atmospheric circulation 大气环流 meridional circulation 经向环流 zonal circulation 纬向环流 Hadley cell 哈得来环流 Walker cell 沃克环流 direct circulation 直接环流 indirect circulation 间接环流［圈］ trade-wind circulation 信风环流 circulation cell 环流圈 local circulation 局地环流 three-cell ［meridional ］ circulation 三圈经向环流 circulation index 环流指数high index 高指数 low index 低指数 index cycle 指数循环 circulation theorem 环流定理 Kelvin's theorem of circulation 开尔文环流定理 Bjerknes circulation theorem 皮叶克尼斯环流定理 cross-equatorial flow 越赤道气流atmospheric center of action 大气活动中心 scaling 尺度分析synoptic scale 天气尺度 planetary scale 行星尺度 meso scale 中尺度 mesoscale model 中尺度模式 general circulation model, GCM 大气环流模式 barotropic model 正压模式 baroclinic model 斜压模式06.天气学synoptic meteorology 天气学 weather 天气 synoptic chart 天气图 6 / 10continuity equation 连续方程 equation of state 状态方程 vorticity equation 涡度方程 divergence equation 散度方程 hydrostatic equation 流体静力方程 3 -equation 3方程 perturbation equation 扰动方程 thermal wind equation 热成风方程 advective equation 平流方程 balance equation 平衡方程 baroclinic process 斜压过程geostrophic adjustment 地转适应 available potential energy 有效位能 geopotentialmeter 位势米 geopotential height 位势高度 inertial instability 惯性不稳定 free convection level 自 由对流高度［atmospheric ］ stability ［大气］稳定度 static stability 静力稳定度 absolutestability 绝对稳定 absolute instability 绝对不稳定 neutral stability 中性稳定conditional instability 条件［性］不稳定 barotropic instability 正压不稳定baroclinic instability 斜压不稳定 latent instability 潜在不稳定conservation of potential vorticity 位涡守恒 z-coordinate z 坐标p-coordinate p 坐标 。

国际贸易、市场营销类课题外文翻译——市场定位策略(Positioning_in_Practice)

国际贸易、市场营销类课题外文翻译——市场定位策略(Positioning_in_Practice)

Positioning in PracticeStrategic Role of MarketingFor large firms that have two or more strategic business units (SBUs), there are generally three levels of strategy: corporate-level strategy, strategic-business-unit-level (or business-level) strategy, and marketing strategy. A corporate strategy provides direction on the company's mission, the kinds of businesses it should be in, and its growth policies. A business-level strategy addresses the way a strategic business unit will compete within its industry. Finally, a marketing strategy provides a plan for pursuing the company's objectives within a specific market segment. Note that the higher level of strategy provides both the objectives and guidelines for the lower level of strategy.At corporate level, management must coordinate the activities of multiple strategic business units. Thus the decisions about the organization's scope and appropriate resource deployments/allocation across its various divisions or businesses are the primary focus of corporate strategy.Attempts to develop and maintain distinctive competencies tend to focus on generating superior financial, capital, and human resources; designing effective organizational structures and processes; and seeking synergy among the firm's various businesses.At business-level strategy, managers focus on how the SBU will compete within its industry. A major issue addressed in business strategy is how to achieve and sustain a competitive advantage. Synergy for the unit is sought across product-markets and across functional department within the unit.The primary purpose of a marketing strategy is to effectively allocate and coordinate marketing resources and activities to accomplish the firm's objectives within a specific product-market. The decisions about the scope of a marketing strategy involve specifying the target market segment(s) to pursue and the breadth of the product line to offered. At this level of strategy, firms seek competitive advantage and synergy through a well-integrated program of marketing mix elements tailored to the needs and wants of customers in the target segment(s).Strategic Role of PositioningBased on the above discussion, it is clear that marketing strategy consists of two parts: target market strategy and marketing mix strategy. Target market strategy consists of three processes: market segmentation, targeting (or target market selection), and positioning. Marketing mix strategy refers to the process of creating a uniqueblend of product, distribution, promotion, and pricing strategies (the four Ps) designed to satisfying the needs and wants of customers. Target market strategy and marketing mix strategy are closely linked and have a strong interdependence. The position of a product identified from the target market strategy serves as a guideline for formulating marketing mix strategy.Market segmentation is the process by which a market is divided into distinct customer subsets of people with similar needs and characteristics that lead them to respond in similar ways to a particular product offerings and strategic marketing programs.Targeting or target market selection is the process of selecting a segment or segments to serve by evaluating the relative attractiveness of each segment, the benefit sought, and the firm's relative business strengths.Finally, positioning is the process of designing product offerings and developing strategic marketing programs which collectively create an enduring competitive advantage in the target market.The concept of target market strategy especially positioning is well-known and widely accepted by most marketing practitioners especially consumer goods managers as useful Atheoretical concepts in formulating marketing mix strategy. In practice, however, marketers tend to bypass formal positioning and go directly to formulate marketing mix strategy. This may be due to the fact that these managers do not know how to obtain perceptual maps, which are maps that show the positions of products on a set of primary customer needs.The objective of this paper is to demonstrate a practical way for marketing practitioners to obtain perceptual maps for positioning and marketing mix strategy formulation. Specifically, perceptual mapping and its relation to positioning are first discussed. This is followed by discussion of statistical techniques that can be used to create perceptual maps. Finally, a example of positioning process by factor analysis is demonstrated.Perceptual Mapping: Identification of StrategicBenefitsPositioning is the perceived fit between a particular product and the needs of the target market, and thus positioning concept must be defined relative to the customer’s needs and competitive offerings.It is one of the most important strategic concepts because it is concerned with differentiation. Positioning reflect the careful efforts of marketing firms to portray the benefits they offer customers and to differentiate themselves from competition. Positioning is critical for a product=s success. Not only must the product deliver the benefits the customer needs, but it must do so better than competition.Effective positioning requires assessing the positions occupied by competing products, determining the important dimensions underlying these positions, and choosing a p osition in the market where the organization’smarketing efforts will have the greatest impact. An essential tool for strategic benefit positioning is perceptual maps.Customer Needs and Perceptual Mapping: Method and ProceduresPerceptual maps represent the positions of products on a set of primary customer needs. Perceptual maps visually summarized the dimensions that customers use to perceive and judge products and identify how competitive products are placed on those dimensions. In practice, marketers need to know the number of dimensions, the names of those dimensions, what more detailed customer needs make up the dimensions, where competition is positioned, and where the ideal position for a new product or for repositioning is.A set of useful consumer behavior model has been developed to handle consumer attitudes toward various brands in a marketplace. Hauser and Urban (1977), in a new-product setting, describe the processing of product attributes as compression into smaller number of aggregate dimensions called Aevaluation criteria. The central idea is that the brands in a market can be represented as a set of points in a multidimensional space. The axes of this space represent the perceived attributes that characterize the stimuli. Two main analytical approaches most frequently used to derive evaluation criteria and build perceptual maps are decompositional methods, based on multidimensional scaling, and compositional methods, based on factor analysis (Lilien and Kotler 1983). Each of these procedures is discussed in the following section.Multidimensional Scaling (MDS)Multidimensional scaling (MDS) is a set of procedures in which a reduced space of product alternatives reflects perceived similarities and dissimilarities between products by the inter-product distances.mensional scaling to create perceptual maps:1.Have customers evaluate existing products according to their relative similarity and form an average proximity matrix whose entries represent the similarities or dissimilarities among the products for each group of customers you wish to analyze.e multidimensional scaling to produce a map in 2, 3, ... dimensions.3.Based on managerial judgments, limitations owing to the number of stimuli, and a plot of Astress select the appropriate number of dimensions.4. Name the dimensions based on the relative position of the stimuli or a regression of the map coordinates on attribute ratings.Multidimensional scaling is a powerful technique, but it must be used with caution. Several issues need to be considered. The first issue is concerned with the number of stimuli (i.e., products) needed. Klabir (1969) showsthat at least eight products are needed to create a good two-dimensional map. Green and Wind (1973) suggest that the number of dimensions should be less than one-third of the number of products. The second issue is concerned with the naming of the dimensions. The analyst generally names the dimensions by using knowledge of the product category to explain best the products= positions. This procedure is arbitrary and involves a high degree of creativity. The final issue is concerned with the number of dimensions. There is little theory to guide the selection of the number of dimensions. However, the stress measure obtained from MDS can be plotted against the number of dimensions to determine when marginal changes in stress are becoming small.Widely used, user-friendly statistical packages such as SAS and SPSS contain the programs for multidimensional scaling. For example, in SPSS, one can obtain a multidimensional scaling analysis from the statistics menu by choosing scale and then multidimensional scaling.Factor AnalysisFactor analysis was originally developed in connection with efforts to identify the major factors making up human intelligence. Educational and psychological researchers did not believe that every test in an educational battery measured a different facet of intelligence. In fact, test scores for certain pairs of tests were highly inter correlated, indicating that a more basic mental ability underlies test performance. Factor analysis was developed to explain these intercorrelations in the test results of a few basic intelligence factors, subsequently identified as verbal ability, quantitative ability, and spatial ability. Since that time, factor analysis has been applied to many other problems and is a frequently used technique in performing product-evaluation analyses in marketing.The basic factor-analysis model assumes that original perceptual ratings about a product are generated by a small number of latent variables, or factors, and that the variance observed in each original perceptual variable is accounted for partly by a set of common factors and partly by a factor specific to that variable. In the construction of a perceptual map by factor analysis, the positions of the products/brands studied can be obtained by averaging the factor scores of the respondents for each product/brand. Factor scores are calculated from the matrix of factor-score coefficients, which describes factor scores as a linear function of the original ratings.To use factor analysis to create perceptual map:1. Have consumers rate all the products/brands under studied, one at a time, on a set of product attributes. You can use Likert scales (scales anchored with strongly agree and strongly disagree) or semantic differential scales (scales with bipolar adjectives) in your questionnaire.2. Analyze the data by factor analysis with rotation (e.g., with varimax rotation). Also request for factor scores for all the products/brands.3. Average the factor scores over all the respondents for each product/brand.4. Use the average factor scores for each product/brand as coordinates to plot the position on the perceptual space. Normally, two-dimensional maps are meaningful and easy to understand. If more than two factors are extracted/identified from the set of product attributes, more than one two-dimensional maps may be generated.5. Use factor loading table, which is an output representing the correlations between the attribute scales and the factors that the computer algorithm identified, to name the factors.6. Theideal line (representing the relative importance of the factor scores in determining attitude toward the brand) can be identified from the multiple regression function with attitude as the dependent variable and factor scores as the independent variables.Factor analysis is a very powerful and useful technique for producing perceptual maps. There are also many software for PC that contains this statistical technique (e.g., SPSS, SAS, BMDP).In this session, we briefly went through the concepts of target market strategy (which consists of market segmentation, targeting, and positioning), strategic brand management, and positioning research. Then we went through the concept and the steps in the data analysis for positioning research.Target Market StrategyTarget market strategy is the process of identifying one (or more target markets) and its (or their) unique positioning(s). Target market strategy consists of (1) market segmentation, (2) targeting, and (3) positioning.Market Segmentation. Market segmentation is the process of segmenting a heterogeneous potential market into a few or several homogeneous segments. In other words, customers in a potential market may have different preferences. As such, it is not effective and efficient to teach all of them by one product and one plan. To be effective and efficient, a manager needs to group the potential customers into group according to their unique preferences and serves one or more of these groups according to the company's strength. The other way to look at market segmentation is that it is the process to test if the potential market is homogeneous in terms of preferences. Good market segmentation should result in segments with the following characteristics: (1) substantiality ( i.e., each segment is large enough), (2) profilability/identifiability/measurability (i.e., each segment can be described in terms of demographic or psychographic characteristics), (3) accessibility (i.e., the media consumption and shopping behavior can be identified), and (4) differential responsiveness (i.e., each segment has a unique preference).Targeting. Targeting or target market selection is the process of selecting one or more segments to be the target market or target markets. The segment(s) is(are) chosen by matching the strengths/ability of the companyto serve the segment with the profit potential in each segment. GE Matrix (market attractiveness versus business position) is a good tool for targeting.There are four targeting strategies that you can use: (1) concentrated or focused targeting strategy (i.e., selecting one large segment to be your target market), (2) multi-segment or differentiated targeting strategy (i.e., selecting two or more large segments to be your target markets with a unique positioning for each of them), (3) mass targeting strategy (i.e., selecting two or more or all segments to be your target market with only one positioning for all of them), and (4) niche targeting strategy (i.e., selecting one small market to be your target market).Positioning. Positioning has two meanings. First, positioning is the most important benefit or benefits desired by the customers in a particular target market. Second, positioning is the process of creating brand image (in terms of benefit or benefits) in the customer's mind through marketing mix strategy (the 4Ps). The brand image must reflect the most important benefit(s) that the target customers want. To position your brand in a target market, you first conduct positioning research to create a perceptual map of competing brands in the target The following note is provided by Prof.Powpaka SamartWhat Is Marketing?STRATEGIC MARKETINGAs you may already know, the main objective of any business is to make profit. On the other hand, there are also non-profit or not-for-profit organizations that exist in the society. Their main objective is to achieve a non-profit objective or to serve a certain cause, e.g., HK Red Cross wants to obtain enough blood to help the patients. These non-profit organizations still need to make money or obtain money. But they do not do it for profit; they do it in order to secure enough resources to help them achieve their non-profit objectives.To achieve their objectives, businesses and non-profit organizations need to have different people to perform different functions. They normally organize people who perform the same function into the same "departments". Accounting, finance, production, R&D, logistics, marketing, and sales are examples of departments that normally exist in a business organization."What is marketing?" Using American Marketing Association's (1985) definition, marketing is "the process of planning and execution of the conception, pricing, distribution, and promotion of goods, services, and ideas to create or facilitate exchanges that satisfy both individual and organizational objectives." Based on the definition, it is quite clear that the definition is inclined toward marketing as a business function (or what marketing people do). In essence, the function of marketing is about identifying the right target market (a group of consumers or business customers) and creating, communicating, and delivering the company's products (which can be goods, services,ideas, or combination of goods, services, and ideas) to the chosen customers. What marketing people do is to plan and execute the marketing plan, which consists of product strategy, pricing strategy, distribution strategy, and communication strategy. The execution of the marketing plan will create or facilitate the exchange or transaction between the target customers and the organization.Then we look into the definition of marketing by AMA in 2004. Marketing is "an organizational function and a set of processes for creating, communicating, and delivering value to customers and for managing customer relationships in ways that benefit the organization and its stakeholders." It is clear from the definition that marketing includes both marketing as a business function (an organizational function) and as a management philosophy/orientation (a set or cross-functional or cross-departmental processes for [a] creating, communicating, and delivering value to the target customer and [b] to manage relationship with customers in ways that benefit the stakeholders). Marketing as a management philosophy requires an integrated effort of every members of the organization to provide superior "value" to the customer and to build, enhance, and maintain "relationship" with (profitable) target customers.When we look at the definition of marketing by AMA (2004), you can see that marketing, as a management philosophy, requires the integration of every function or department to work together to satisfy the target customers. The target customer is the focus of the company's operations. Everybody in the company (1) works together to create, communicate, and deliver value to the customer and (2) manages the relationship with customers in ways that benefits the company and its stakeholders.We then discussed about the formula of value to demonstrate that customer value creation comes from the integrated effort of every employee of the firm.Value = quality/price + relationshipsQuality: Quality represents everything that customers get from buying your product. As such, quality must be defined by your customers. There are two types of quality: (1) objective quality (i.e., actual quality as can be tested in the lab according to the specification) and (2) perceived or subjective quality (i.e., quality as "perceived" or "believed" by the customers). R&D and production staffs make sure that the objective quality of the company's products is acceptable. Quality standards and measures such as TQM, QC, ISO, etc are used to ensure objective quality. Marketing people use integrated marketing communication (IMC) to build perceived quality in the mind of the customers. It is important that there is a match between objective and perceived quality.Price: One of the determinants of price is cost. Today, there are two major sources of cost reduction: (1) global sourcing and (2) logistics management. Global sourcing concerns with two consecutive decisions: (1) tomake or to buy (i.e., to manufacture the products by yourself or to sub-contract other people to produce for you), and (2) where to make or where to buy. Proper global sourcing can give cost advantage to the firm. Logistics concerns with the strategic movement and storage of products into the firm, inside the firm, and out of the firm. Purchasing or inbound logistics concerns with the movement and storage of raw materials, processed materials, and component parts into the firm. Manufacturing support of intra logistics concerns with the movement and storage of semi-finished products inside the firm. Finally, physical distribution or outbound logistics concerns with the movement of finished products from the firm to its customers. The main concept of logistics is (1) to provide the desired service level to both internal and external customers and (2) at the lowest total cost. A logistics system consists of 3 performance cycle: (1) inbound logistics (or purchasing), (2) intra or inside logistics (or manufacturing support), and outbound logistics (or physical distribution). A good logistics system not only reduces the cost for the company but also provides competitive advantage for the company. In other words, a good logistics system can give a company sustainable competitive advantage by providing appropriate level of service at the lowest total cost.The service level in logistics consists of:1. Availability2. Operational performancea. Speedb. Consistencyc. Flexibilityd. Malfunction and recovery3. ReliabilityThe costs in logistics include:1. Order management costs2. Inventory management costs3. Material handling costs4. Transportation costs5. Warehousing costsRelationships: There are two types of relationships: (1) relationship with your customers (i.e., relationship marketing and customer relationship management or CRM) and (2) relationships with suppliers and channelmembers (i.e., strategic alliance/partnership). Strong relationships with both customers and suppliers/channel members are important in the value creation process for the customers.A company that adopts marketing as its management philosophy or company orientation will try to survive and grow in long-term by focusing on satisfying the needs and wants (i.e., preferences to be more accurate) through the integrated effort of everybody in the firm. As such, a marketing-oriented company has the following characteristics:* Long-term focus (i.e., profit and growth as a result of customer loyalty/long-lasting relationship)* Customer focus or customer orientation (i.e., understanding the target customers' needs/wants/problems and their alternatives now and in the future)* Competitor focus or customer orientation (i.e., understanding the major competitors' objectives and strategies now and in the future)* Inter-functional or inter-departmental coordination (i.e., every employee takes full responsibility of the success/failure of the firm)。

医学物理实验_山东大学中国大学mooc课后章节答案期末考试题库2023年

医学物理实验_山东大学中国大学mooc课后章节答案期末考试题库2023年

医学物理实验_山东大学中国大学mooc课后章节答案期末考试题库2023年1.日常生活中的表面吸附现象有：The surface adsorption phenomena in dailylife are as follows:参考答案:面粉洗葡萄Washing grapes with flour_活性炭过滤水Activated carbonfilter water_水面上的油膜Oil film on water2.杨氏弹性模量E仅决定于材料本身的性质，而与外力ΔF，物体的长度L以及截面积S的大小无关，它是表征固体材料性质的一个重要物理量。

Young's modulus of elasticity e is only determined by the properties of thematerial itself, but has nothing to do with the external force Δ F, the length L of the object and the cross section product S. It is an important physicalquantity to characterize the properties of solid materials.参考答案:正确3.精密度是与“真值”之间的一致程度，是系统误差与随机误差的综合。

Precision is the degree of consistency with "true value", and is the synthesis of systematic error and random error.参考答案:错误4.以下说法正确的是：Which statement below is correct参考答案:在一定的温度下，它的旋光率与入射光波长的平方成反比，且随波长的减少而迅速增大，这现象称为旋光色散。

phase-field modeling

phase-field modeling

Phase field modelsFrom Wikipedia, the free encyclopediaJump to: navigation, searchA phase field model is a mathematical model for solving interfacial problems. It has mainly been applied to solidification dynamics,[1]but it has also been applied to other situations such as viscous fingering,[2]fracture dynamics, [3] vesicle dynamics,[4] etc.The method substitutes boundary conditions at the interface by a partial differential equation for the evolution of an auxiliary field (the phase field) that takes the role of an order parameter. This phase field takes two distinct values (for instance +1 and −1) in each of the phases, with a smooth change between both values in the zone around the interface, which is then diffuse with a finite width.A discrete location of the interface may be defined as the collection of all points where the phase field takes a certain value (e.g., 0).A phase field model is usually constructed in such a way that in the limit of an infinitesimal interface width (the so-called sharp interface limit) the correct interfacial dynamics are recovered. This approach permits to solve the problem by integrating a set of partial differential equations for the whole system, thus avoiding theexplicit treatment of the boundary conditions at the interface.Phase field models were first introduced by Fix[5] and Langer,[6] and have experienced a growing interest in solidification and other areas.Contents∙ 1 Equations of the Phase field modelo 1.1 Variational formulationso 1.2 Sharp interface limit of the Phase field equations∙ 2 Multi Phase Field Models∙ 3 Software∙ 4 Further reading∙ 5 References[edit] Equations of the Phase field modelPhase field models are usually constructed in order to reproduce a given interfacial dynamics. For instance, in solidification problems the front dynamics is given by a diffusion equation for either concentration or temperature in the bulk and some boundary conditions at the interface (a local equilibrium condition and a conservation law),[7] which constitutes the sharp interface model.A two phase microstructure and the order parameter φ profile is shown on a line across the domain. Gradual change of order parameter from one phase to another shows diffuse nature of the interface.A number of formulations of the phase field model are based on a free energy functional depending on an order parameter (the phase field) and a diffusive field (variational formulations). Equations of the model are then obtained by using general relations of Statistical Physics. Such a functional is constructed from physical considerations, but contains a parameter or combination of parameters related to the interface width. Parameters of the model are then chosen by studying the limit of the model with this width going to zero, in such a way that one can identify this limit with the intended sharp interface model.Other formulations start by writing directly the phase field equations, without referring to any thermodynamical functional (non-variational formulations). In this case the only reference is the sharp interface model, in the sense that it should be recovered when performing the small interface width limit of the phase field model.Phase field equations in principle reproduce the interfacial dynamics when the interface width is small compared with the smallest length scale in the problem. In solidification this scale is the capillary length d o, which is a microscopic scale. From a computational point of view integration of partial differential equations resolving such a small scale is prohibitive. However, Karma and Rappel introduced the thin interface limit,[8] which permitted to relax this condition and has opened the way to practical quantitative simulations with phase field models. With the increasing power of computers and the theoretical progress in phase field modelling, phase field models have become a useful tool for the numerical simulation of interfacial problems.[edit] Variational formulationsA model for a phase field can be constructed by physical arguments if one have an explicit expression for the free energy of the system. A simple example for solidification problems is the following:where φ is the phase field, u = e / e0 + h(φ) / 2, e is the local enthalpy per unit volume, h is a certain polynomial function of φ, and e0 = L2 / T M c p (where L is the latent heat, T M is the melting temperature, and c p is the specific heat). The term withcorresponds to the interfacial energy. The function f(φ) is usually taken as a double-well potential describing the free energy density of the bulk of each phase, which themselves correspond to the two minima of the function f(φ). The constants K and h0 have respectively dimensions of energy per unit length and energy per unitvolume. The interface width is then given by . The phase field model can then be obtained from the following variational relations:[9]where D is a diffusion coefficient for the variable e, and η andare stochastic terms accounting for thermal fluctuations (and whose statistical properties can be obtained from the fluctuation dissipation theorem). The first equation gives an equation for the evolution of the phase field, whereas the second one is a diffusion equation, which usually is rewritten for the temperature or for the concentration (in the case of an alloy). These equations are, scaling space with l and times with l2 / D:where is the nondimensional interface width, α = Dτ / W2h0,and , are nondimensionalized noises.[edit] Sharp interface limit of the Phase field equationsA phase field model can be constructed to purposely reproduce a given interfacial dynamics as represented by a sharp interface model. In such a case the sharp interface limit (i.e. the limit when the interface width goes to zero) of the proposed set of phase field equations should be performed. This limit is usually taken by asymptotic expansions of the fields of the model in powers of the interface width . These expansions are performed both in the interfacial region (inner expansion) and in the bulk (outer expansion), and then are asymptotically matched order by order. The result gives a partial differential equation for the diffusive field and a series of boundary conditions at the interface, which shouldcorrespond to the sharp interface model and whose comparison with it provides the values of the parameters of the phase field model.Whereas such expansions were in early phase field models performed up to the lower order in only, more recent models use higher order asymptotics (thin interface limits) in order to cancel undesired spureous effects or to include new physics in the model. For example, this technique has permitted to cancel kinetic effects,[8] to treat cases with unequal diffusivities in the phases,[10] to model viscous fingering[2] and two-phase Navier–Stokes flows,[11] to include fluctuations in the model,[12] etc.[edit] Multi Phase Field ModelsMultiple order parameters describe a polycrystalline material microstructure.In multi a phase field model microstructure is described by set of order parameters each one is related to a specific phase or crystallographic orientation. This model is mostly used for solid state phase transformations where multiple grains evolve (e.g. grain growth, recrystallization or first order transformation like austenite to ferrite in ferrous alloys.[edit] Software∙The Mesoscale Microstructure Simulation Project (MMSP) is a collection of c++ classes for grid-based microstructure simulation. ∙The Microstructure Evolution Simulation Software (MICRESS) is a multi-phase field simulation package developed at RWTH-Aachen.[edit] Further reading∙R. Gonzalez-Cinca et al., in Advances in Condensed Matter and Statistical Mechanics, ed. by E. Korucheva and R. Cuerno, NovaScience Publishers (2004) a review on phase field models.∙L-Q Chen, Annual Review of Materials Research, Vol. 32: 113-140 (2002) Phase field models in solidification∙N. Moelans, B. Blanpain, P.Wollants, Calphad, Vol. 32: 268-294 (2008) An introduction to phase-field modeling for microstructure evolution∙I. Steinbach:Phase-field models in Materials Science –Topical Review, Modelling Simul. Mater. Sci. Eng. 17 (2009)073001∙S.G.Fries, B.Böttger, J.Eiken,I.St einbach:Upgrading CALPHAD to microstructure simulation: the phase-field method, Int.J.Mat.Res100(2009)2∙R. Qin and H. K. D. H. Bhadeshia, a critical assessment of the phase field method, 2010, published in Materials Science andTechnology.[edit] References1.^WJ. Boettinger et al. Annual Review of Materials Research Vol. 32:163-194 (2002)2.^ a b R. Folch et al. Phys. Rev. E 60, 1734 - 1740 (1999)3.^ A. Karma et al. Phys. Rev. Lett. 87, 045501 (2001)4.^T. Biben et al. Phys. Rev. E 72, 041921 (2005)5.^ G.J. Fix, in Free Boundary Problems: Theory and Applications, Ed.A. Fasano and M. Primicerio, p. 580, Pitman (Boston, 1983).6.^ J.S. Langer, Models of pattern formation in first–order phasetransitions, in Directions in Condensed Matter Physics p. 165, Ed. G.Grinstein and G. Mazenko, World Scientific, Singapore, (1986).7.^J.S. Langer, Rev. Mod. Phys. 52, 1 (1980)8.^ a b A. Karma and W.J. Rappel Phys. Rev. E 57, 4323 - 4349 (1998)9.^P.C. Hohenberg and B.I. Halperin, Rev. Mod. Phys. 49, 435 (1977)10.^G. B. McFadden et al., Physica D 144, 154-168 (2000)11.^ D. Jacqmin, J. Comput. Phys. 155,96-127 (1999)12.^R. Benítez and L. Ramírez-Piscina Phys. Rev. E 71, 061603 (2005)。