ustc 梯度算子 算符方程式:究竟是在对哪一个标量场进行微分 ...
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2012年8月17日 - phymath999 ... 在每点上物体中原子的速度便是位置函数的矢量。 ..... 的動力性質是由波方程式來決定，現在我們無法由波的介質組成結構（如繩子粒子之於... ... 当熱能比能級間隔小得多时，这样的一個自由度就說成是被“凍結”了。 ..... 高分子材料小形變下橡膠內能幾乎不變, · Josh Krause vix term structure · vix term ...轉為繁體網頁
phymath999: 针对全息测量物体形变的缺点，采用全息二次 ...
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2014年2月22日 - 条纹计数法、零级条纹法和等倾条纹法。 ... 本文采用全息二次曝光对物体形变测量，轉為繁體網頁
Blackbody Radiation
www.launc.tased.edu.au/.../blackbody1.ht...
Launceston College, Tasmania
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Anything which is "hot" will absorb and emit electromagnetic radiation. That is ... Radiation from exterior. - less bright than interior. radiation. Brightness. HEAT.
BLACK BODY RADIATION - MAX PLANCK topics
Continuous spectra
Examples -
CLOSELY RELATED - RED HOT STOVE ELEMENTS, INFRARED RADIATION FROM YOU.
Anything which is "hot" will absorb and emit electromagnetic radiation. That is what we mean when we say a stove element is "red hot" or a light filament is "white hot".
What is "hot"? Any temperature above -2730C or O kelvin.
Radiation coming in will impinge on the material's electrons, some will be reflected, some absorbed. Equally, the material's electrons are accelerating and can emit radiation, not much if cool, lots if warm. ( Whatever cool and warm are! ) Solids have electrons in energy bands rather than in the individual levels of single atoms. Metals are extreme examples of this characteristic. The electrons can therefore behave very freely - just as they do in a plasma - a gas of ionised particles such as the Sun. This allows them to behave as antennae and reflect etc.
All "hot" bodies of the same temperature have the same shape radiation graph with a peak at a characteristic point absolutely dependent on the temperature. However, different materials have different brightnesses of radiation. Tungsten in a filament lamp emits the same shape curve but at a slightly different strength than a ceramic at the same temperature.
We humans are at a temperature of 370C or 310 K. We therefore emit radiation with the peak in the infrared at 9.3 μm. We also emit microwaves and radio waves. A hot plate at 4000C or 673 K will have a peak at 4.3 μm but will also emit a little in the visible red. It will appear red hot!
(Infrared detectors "see" humans extremely well in the dark or cold because humans are brighter than their cooler surroundings. Infrared detectors are therefore common on Search and Rescue and military machines.)
Is there a greatest ( brightest ) curve? YES - that of a PERFECTLY BLACK OBJECT- one which will perfectly absorb every littlest bit of light ( radiation ) landing on it.
Most people know that black objects warm up faster than white objects in the sun. What most do not realise is that black things cool down faster than white ones when out of the sun! ( Chip cooling fins on ICs should be painted black, insulation foil in walls of houses and in vacuum flasks are white - silver ( same thing ) for these reasons. )
PROBLEM - How to make a Black Body ? - Solution - by making a CAVITY RADIATOR.
You can see that light entering the door gets in BUT FINDS IT HARD TO ESCAPE. The gap is a black body!
Further, the interior radiation must be in an equilibrium state - no light can enter, none can escape so the emissions must balance the absorptions, and the light must be as bright as is possible for the temperature of the room.
When, in practice, hollow metals or ceramics are heated, the radiation from a tiny hole is indeed brighter (more energy per second for the volume inside) than the surface and IS Black Body (BB) . You have seen or felt this no doubt when looking into the family fire when the hottest radiation clearly comes from gaps between red hot coals. ( Hottest - read brightest or most intense or most energy per second for the volume. )
C19th PROBLEM
How to match the known emitted radiation of a "hot" object with theory - "The Black Body problem".
Situation late C19th.
1900-01 - he found a method of getting the correct graph. How he got there later horrified him. He "incorrectly" used Boltzmann's entropy theory by not completing a limiting process as used in calculus. For those who know calculus, taking limits smooths, makes continuous, processes. As it was, the theory was discontinuous, lumpy. Had he - he would have ended up back at the Rayleigh-Jeans' result, which was wrong. In essence, he had to use LITTLE BITS OF ENERGY IN EMISSION AND ABSORPTION . Each little bit was associated with a frequency.
读《电学计量技术发展综述》有感
Continuous spectra
Examples -
- Star spectra are nearly Black Body
- Radiation out of an oven or a blast furnace
- Radiation coming out of human mouths, noses and other orifices
- The Universe
CLOSELY RELATED - RED HOT STOVE ELEMENTS, INFRARED RADIATION FROM YOU.
Anything which is "hot" will absorb and emit electromagnetic radiation. That is what we mean when we say a stove element is "red hot" or a light filament is "white hot".
What is "hot"? Any temperature above -2730C or O kelvin.
Radiation coming in will impinge on the material's electrons, some will be reflected, some absorbed. Equally, the material's electrons are accelerating and can emit radiation, not much if cool, lots if warm. ( Whatever cool and warm are! ) Solids have electrons in energy bands rather than in the individual levels of single atoms. Metals are extreme examples of this characteristic. The electrons can therefore behave very freely - just as they do in a plasma - a gas of ionised particles such as the Sun. This allows them to behave as antennae and reflect etc.
All "hot" bodies of the same temperature have the same shape radiation graph with a peak at a characteristic point absolutely dependent on the temperature. However, different materials have different brightnesses of radiation. Tungsten in a filament lamp emits the same shape curve but at a slightly different strength than a ceramic at the same temperature.
(Infrared detectors "see" humans extremely well in the dark or cold because humans are brighter than their cooler surroundings. Infrared detectors are therefore common on Search and Rescue and military machines.)
Is there a greatest ( brightest ) curve? YES - that of a PERFECTLY BLACK OBJECT- one which will perfectly absorb every littlest bit of light ( radiation ) landing on it.
PROBLEM - How to make a Black Body ? - Solution - by making a CAVITY RADIATOR.
Imagine you are terrified by your big sister/brother - pretty easy unless you are the eldest.( If you are the eldest - try your little sibling .) You are to go down the corridor past their bedroom door which is slightly ajar on your way bed. IT IS SPOOKY. The gap is BLACK, Fearsome Creatures live in there!!
You can see that light entering the door gets in BUT FINDS IT HARD TO ESCAPE. The gap is a black body!
Further, the interior radiation must be in an equilibrium state - no light can enter, none can escape so the emissions must balance the absorptions, and the light must be as bright as is possible for the temperature of the room.
When, in practice, hollow metals or ceramics are heated, the radiation from a tiny hole is indeed brighter (more energy per second for the volume inside) than the surface and IS Black Body (BB) . You have seen or felt this no doubt when looking into the family fire when the hottest radiation clearly comes from gaps between red hot coals. ( Hottest - read brightest or most intense or most energy per second for the volume. )
How to match the known emitted radiation of a "hot" object with theory - "The Black Body problem".
Situation late C19th.
- Maxwell had set up superb equations describing light.
- Bolzmann and many others had set up descriptions of heat and temperature, - thermodynamics.
- Excellent measurements of BB curve had been made by 1898
- The TOTAL energy persecond associated with a temperature was evaluated
- The PEAK point associated with a temperature had been found. Wien's Law.
- No one could exactly match Maxwell's equations with the BB curve - two attempts were the Rayleigh /Jean approach ( this approach looked at standing waves in the cavity ) which worked at low frequencies but was an "Ultra Violet Catastrophe" and that of Wien which worked at high frequencies but went wrong at lower values.
ΔE = h f
h = constant, Planck's Constant = 6.623 x 10-34 Js
He spent years trying to regularize ( "classicise" ) the maths but failed. Einstein was the one who recognised that a whole new physics was evolving - quantum physics. He used the ideas further in solving the Photoelectric Effect and developing Bose-Einstein statistics.
THE TEMPERATURE OF THE UNIVERSE
The Universe is the perfect cavity - it has no leaks and contains all of its radiation. It therefore has a temperature - a Black Body radiation spectrum belonging to a certain temperature. That temperature is 2.728 K. The curve is in the microwave region and is small but real. The radiation curve is near proof that the Universe had a very hot beginning ( the Big Bang - though now replaced by the "Inflation Theory".)
The Universe is now thought to have been "born" about 12-15 billion years ago and occupied no volume at first. It rapidly expanded and some of the radiation condensed into matter. As the Universe has continued to expand, the remnant radiation has stretched with it lengthening the wavelength and so "cooling" it - ie associating it with a lower BB temperature.
History
- Einstein's General Relativity - 1915
- Expansion of the Universe - Hubble - 1920's
- George Gamow - applied expansion to GR and came up with a tentative "Hot beginning". Predicted a cool BB radiation to be present even now.
- Penzias and Wilson, 1964, using a Bell Laboratory satellite tracking antenna discovered a strange microwave background radiation, that of the Universe itself. ( They had trouble with a pair of homing pigeons nesting in the antenna that radiated in the microwave region because of their body temperature and producing errors in their measurements.)
- Large accelerators in France/Switzerland (CERN) and USA and elsewhere create the temperatures (energies) of the very early Universe testing the physics of that era.
- 1992 COBE, ref 1, satellite makes a detailed map of this radiation throughout the sky - temperature 2.728 K. Finds slight temperature variations in different directions.
- The small variations in the BB radiation currently being examined for clues as to the early Universe's history. The slight variations imply a "lumpiness" throughout the Universe somewhere in the first femtosecond or so. These have been collated into a new map - more detailed than COBE and released in February 2003. This data now gives the age of our Universe as 13.7 billion years with good precision and confirming "The Inflation Model" as the probable mechanism.( See picture below.)
- Planck Telescope makes a much higher resolution scan of the Universe
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G o o g l e 在網路漫遊時會自動將檔案轉換成 HTML 網頁。
G o o g l e 在網路漫遊時會自動將檔案轉換成 HTML 網頁。
读《电学计量技术发展综述》有感
文中提到了电学中很重要的一个概念量子基准技术：
国际单位制SI的7个基本单位中与电磁量有关的基本单位是(A) ,但在实际工作中长期维持高度稳定的电流标准相当不容易,而电压单位和电阻电位则可以用标准电池与标准电阻作为实物标准量值来保存,便于开展工作。另一方面,有了电压单位和电阻单位,就可用实验的方法导出所有电磁学单位,因此世界各国均把电压单位和电阻单位作为保存和复现电磁单位的实际手段。电压单位和电阻单位是电磁学单位中最重要的两个单位,目前这两个电学单位都实现了量子基准。
一是约瑟夫森电压基准，
二是量子化霍尔电阻自然基准。
下面我想谈谈量子计量的发展
量子物理学阐明了各种微观粒子的运动规律，特别是微观粒子的态和能级的概念。按照量子物理学，宏观物体中的微观粒子如果处于相同的微观态，其能量有相同的确定值，也就是处于同一能级上。当粒子在不同能级之间发生量子跃迁时，将伴随着吸收或发射能量等于能级差DE的电磁波能量子，也就是光子。而且电磁波频率 n 与 DE之间满足普朗克公式, 即两者之间成正比，而比例系数为普朗克常数h。也就是说，电磁波的频率反映了能级差的数量。值得注意的是，宏观物体中基本粒子的能级结构与物体的宏观参数，如形状、体积、质量等等并无明显关系。因此，即使物体的宏观参数随时间发生了缓慢变化，也不会影响物体中微观粒子的量子跃迁过程。这样，如果利用量子跃迁现象来复现计量单位，就可以从原则上消除各种宏观参数不稳定产生的影响，所复现的计量单位不再会发生缓慢漂移，计量基准的稳定性和准确度可以达到空前的高度。更重要的一点是量子跃迁现象可以在任何时间、任何地点用原理相同的装置重复产生，不象实物基准是特定的物体，一旦由于事故而毁伤，就不可能再准确复制。因此用量子跃迁复现计量单位对于保持计量基准量值的高度连续性也有重大的价值。习惯上，此类用量子现象复现量值的计量基准统称为量子计量基准。
第一个付诸实用的量子计量基准是1960年国际计量大会通过采用的86Kr光波长度基准。其原理是利用86Kr原子在两个特定能级之间发生量子跃迁时所发射的光波的波长作为长度基准。此种基准不象原来的X形原器米尺实物基准那样，长度量值受环境温度、气压等因素的影响，其准确度比实物基准高出近百倍，达到10-9量级。第二个量子计量基准，也是最著名和最成功的一种量子计量基准，是1967年在国际上正式启用的铯原子钟。此种基准用铯原子在两个特定能级之间的量子跃迁所发射和吸收的无线电微波的高准确频率作为频率和时间的基准，以代替原来用地球的周期运动导出的天文时间基准。尽管地球这个实物庞大无比，但其各种宏观参数亦在缓慢地变化，因而其运动的稳定性并不算很高，仅为10-8量级。而近年来铯原子钟的准确度已达到10-14量级，比地球运动的稳定性高了5到6个数量级，几百万年才有可能相差一秒，充分说明了量子计量基准的重大优越性。铯原子钟的巨大成功在天文学、通信技术以至全球定位技术、导弹发射等军事应用方面均得到了卓越的应用。最近有人根据实验数据提出用钙离子的长寿命能级之间的量子跃迁，可把原子钟的准确度再提高一步，达到10-15量级。一些其他更有前途的方案，如激光冷却的铯原子喷泉等，也在发展之中。近年来由于激光技术的飞速发展，使人们对长寿命能级的知识不断增加，制成了一系列极稳定的激光器，其波长的稳定性达到10-12量级，并于1983年替代了86Kr光波长度基准而成为新的更高水平的量子长度基准。与本世纪上半叶还在使用的X型原器米尺实物基准相比，真是不可同日而语了。
随着人们对各种量子跃迁的认识不断深入，量子计量基准已不再局限于复现长度与时间这两种基本单位。80年代以来，电学的量子计量基准也得到了飞速的发展。两种荣获诺贝尔物理学奖的重大发现导致了约瑟夫森电压量子基准和量子化霍尔电阻基准的的建立。1988年国际计量委员会已建议从1990年1月1日起在世界范围内启用约瑟夫森电压标准及量子化霍尔电阻标准以代替原来的由标准电池和标准电阻维持的实物基准，并给出这两种新标准中所涉及的约瑟夫森常数KJ及冯克里青常数RK的国际推荐值。从几年来的实践结果来看，1988年国际计量委员会的建议是十分有效的。采用新方法后电压单位和电阻单位的稳定性和复现准确度提高了两到三个数量级。
目前，各国的计量研究院正在努力攻克经典计量学中的顽固堡垒--用某种量子计量基准来代替尚在使用的铂铱合金千克砝码实物基准。此实物基准是上一世纪制成的，当时估计其准确度为10-9量级，在19世纪的各种计量基准中首屈一指。可惜的是其后陆续发现了不少因素会使其保存的质量量值不断发生变化。例如该砝码尽管不易氧化，但其表面仍会吸附一些肉眼无法察觉的气体分子和其他杂物，甚至其内部也会吸附氢气等气体。这些过程使该砝码质量的增加量可能已达到了十多微克（1×10-8以上)。仔细的清洗过程可以减少此种被吸附的杂物，但过一段时间又会发生类似过程。为了摆脱此种困境，亦应该用某种适当的量子计量基准来代替这一已明显跟不上时代步伐的实物基准。目前对这一十分迫切的课题已提出了若干解决方案。例如用高度提纯的硅晶体中的硅原子质量来作为新的量子质量基准就是一种有希望的方法，其关键步骤是实际计数出硅晶体中原子的数目。但这一方案虽经多年探索，准确度还只达到10-8量级，尚未能直接取代铂铱合金砝码。还有一种办法是利用约瑟夫森电压和量子化霍尔电阻导出量子电功率基准，再经过速度及重力导出质量量值。从原则上说也算是一种量子质量基准。尽管这种方案构思十分巧妙，但稍嫌复杂，目前的准确度也只能达到10-8量级。国际计量局已明确号召各国的计量科学家用各种各样的方案来攻克量子质量基准这一难关，但看起来要到21世纪方有可能见到有实用价值的成果。
可以预见，量子计量基准将为我们提供前所未有的测量准确度，不断发展新型的量子计量标准成为人们不懈的追求。在新世纪各国激烈的技术竞争中，量子计量基准将起着越来越大的作用
第一个付诸实用的量子计量基准是1960年国际计量大会通过采用的86Kr光波长度基准。其原理是利用86Kr原子在两个特定能级之间发生量子跃迁时所发射的光波的波长作为长度基准。此种基准不象原来的X形原器米尺实物基准那样，长度量值受环境温度、气压等因素的影响，其准确度比实物基准高出近百倍，达到10-9量级。第二个量子计量基准，也是最著名和最成功的一种量子计量基准，是1967年在国际上正式启用的铯原子钟。此种基准用铯原子在两个特定能级之间的量子跃迁所发射和吸收的无线电微波的高准确频率作为频率和时间的基准，以代替原来用地球的周期运动导出的天文时间基准。尽管地球这个实物庞大无比，但其各种宏观参数亦在缓慢地变化，因而其运动的稳定性并不算很高，仅为10-8量级。而近年来铯原子钟的准确度已达到10-14量级，比地球运动的稳定性高了5到6个数量级，几百万年才有可能相差一秒，充分说明了量子计量基准的重大优越性。铯原子钟的巨大成功在天文学、通信技术以至全球定位技术、导弹发射等军事应用方面均得到了卓越的应用。最近有人根据实验数据提出用钙离子的长寿命能级之间的量子跃迁，可把原子钟的准确度再提高一步，达到10-15量级。一些其他更有前途的方案，如激光冷却的铯原子喷泉等，也在发展之中。近年来由于激光技术的飞速发展，使人们对长寿命能级的知识不断增加，制成了一系列极稳定的激光器，其波长的稳定性达到10-12量级，并于1983年替代了86Kr光波长度基准而成为新的更高水平的量子长度基准。与本世纪上半叶还在使用的X型原器米尺实物基准相比，真是不可同日而语了。
随着人们对各种量子跃迁的认识不断深入，量子计量基准已不再局限于复现长度与时间这两种基本单位。80年代以来，电学的量子计量基准也得到了飞速的发展。两种荣获诺贝尔物理学奖的重大发现导致了约瑟夫森电压量子基准和量子化霍尔电阻基准的的建立。1988年国际计量委员会已建议从1990年1月1日起在世界范围内启用约瑟夫森电压标准及量子化霍尔电阻标准以代替原来的由标准电池和标准电阻维持的实物基准，并给出这两种新标准中所涉及的约瑟夫森常数KJ及冯克里青常数RK的国际推荐值。从几年来的实践结果来看，1988年国际计量委员会的建议是十分有效的。采用新方法后电压单位和电阻单位的稳定性和复现准确度提高了两到三个数量级。
目前，各国的计量研究院正在努力攻克经典计量学中的顽固堡垒--用某种量子计量基准来代替尚在使用的铂铱合金千克砝码实物基准。此实物基准是上一世纪制成的，当时估计其准确度为10-9量级，在19世纪的各种计量基准中首屈一指。可惜的是其后陆续发现了不少因素会使其保存的质量量值不断发生变化。例如该砝码尽管不易氧化，但其表面仍会吸附一些肉眼无法察觉的气体分子和其他杂物，甚至其内部也会吸附氢气等气体。这些过程使该砝码质量的增加量可能已达到了十多微克（1×10-8以上)。仔细的清洗过程可以减少此种被吸附的杂物，但过一段时间又会发生类似过程。为了摆脱此种困境，亦应该用某种适当的量子计量基准来代替这一已明显跟不上时代步伐的实物基准。目前对这一十分迫切的课题已提出了若干解决方案。例如用高度提纯的硅晶体中的硅原子质量来作为新的量子质量基准就是一种有希望的方法，其关键步骤是实际计数出硅晶体中原子的数目。但这一方案虽经多年探索，准确度还只达到10-8量级，尚未能直接取代铂铱合金砝码。还有一种办法是利用约瑟夫森电压和量子化霍尔电阻导出量子电功率基准，再经过速度及重力导出质量量值。从原则上说也算是一种量子质量基准。尽管这种方案构思十分巧妙，但稍嫌复杂，目前的准确度也只能达到10-8量级。国际计量局已明确号召各国的计量科学家用各种各样的方案来攻克量子质量基准这一难关，但看起来要到21世纪方有可能见到有实用价值的成果。
可以预见，量子计量基准将为我们提供前所未有的测量准确度，不断发展新型的量子计量标准成为人们不懈的追求。在新世纪各国激烈的技术竞争中，量子计量基准将起着越来越大的作用
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