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FreeSandal | 輕。鬆。學。部落客 | 第 261 頁

勇闖新世界︰ W!o《卡夫卡村》變形祭︰感知自然‧尖端‧四

假使我們閱讀

LPS25H 的『數據表』 Data Sheet ︰

Description

The LPS25H is an ultra compact absolute piezoresistive pressure sensor. It includes a monolithic sensing element and an IC interface
able to take the information from the sensing element and to provide a digital signal to the external world.

The sensing element consists of a suspended membrane realized inside a single mono-silicon substrate. It is capable to detect the absolute pressure and is manufactured with a dedicated process developed by ST.

The membrane is very small compared to the traditionally built silicon micromachined membranes. Membrane breakage is prevented
by an intrinsic mechanical stopper.

The IC interface is manufactured using a standard CMOS process that allows a high level of integration to design a dedicated circuit which is trimmed to better match the sensing element
characteristics.

The LPS25H is available in a cavity holed LGA package (HCLGA). It is guaranteed to operate over a temperature range extending from -30 °C to +105 °C. The package is holed to allow external pressure to reach the sensing element.

Key Features

  • 260 to 1260 mbar absolute pressure range
  • High-resolution mode: 1 Pa RMS
  • Low power consumption:
  • Low resolution mode: 4 μA
  • High resolution mode: 25 μA
  • High overpressure capability: 20x full scale
  • Embedded temperature compensation
  • Embedded 24-bit ADC
  • Selectable ODR from 1 Hz to 25 Hz
  • SPI and I²C interfaces
  • Embedded FIFO
  • Supply voltage: 1.7 to 3.6 V
  • High shock survivability: 10,000 g
  • Small and thin package
  • ECOPACK® lead-free compliant

LPS25H

 

,或好奇於『壓阻效應Piezoresistive effect

壓阻效應是用來描述材料在受到機械式應力下所產生的電阻變化。不同於壓電效應,壓阻效應只產生阻抗變化,並不會產生電荷。

要如何用來量測『大氣壓力』?也許引用一段圖文將能解惑的耶!

 

8.4.5 Pressure Microsensors

Pressure microsensors were the first type of silicon micromachined sensors to be developed in the late 1950s and early 1960s.  Consequently, the pressure microsensors represent probably the most mature silicon micromechanical device with widespread commercial availability today.  ……

基本壓力感測器構造
Figure 8.27 Basic types of silicon pressure sensors based on a vertical deflection: (a) piezoresistive (polysilicon) and (b) capacitive (single-crystal silicon)

The two most common methods to fabricate pressure microsensors are bulk and surface micromachining of polysilicon. Silicon diaphragms can be made using either technique as described earlier. Figure 8.27 illustrates the basic principles of a piezoresistive sensor
and a capacitive pressure sensor.

The deflection in the diaphragm can be measured using piezoresistive strain gauges located in the appropriate region of maximum strain, as shown in Figure 8.27(a). The strain gauges are usually made from doped silicon and are designed in pairs with a read-out circuit such as a Wheatstone bridge. The change in strain can be related to the applied pressure ( P - P_0 ) and stored in a lookup table. The precise relationship depends on the relevant piezoresistive coefficient \Pi of the diaphragm material.

V_{out}  \propto \ \Delta R \ \propto \Pi ( P - P_0 )      (8.32)

A single crystal of silicon is a desirable material to use for the diaphragm because neither creep nor hysteresis occurs. The piezoresistive constant ( \Pi ) is typically +138.1 pC/N
and that makes measuring pressure in the range of 0 to 1 MPa relatively straightforward.

Figure 8.27(b) shows the general arrangement of a single-crystal silicon pressure sensor with capacitive pickup. In this case, a capacitive bridge can be formed with two reference capacitors and the output voltage is related to the deflection of the membrane \Delta x and hence the applied pressure ( P - P_0  ).

V_{out} \propto \ \Delta C \propto \ \Delta x \propto \  (P - P_0)      (8.33)

In this case, the accurate positioning of the pickup electrodes is crucial. By controlling the background pressure P_0 , it is possible to fabricate the following basic types of pressure sensors:

• An absolute pressure sensor that is referenced to a vacuum ( P_0 = 0 )

• A gauge-type pressure sensor that is referenced to atmospheric pressure ( P_0 = 1 \ atm )

• A differential or relative type ( P_0 is constant).

─── 引自

《 Microsensors, MEMS, and Smart Devices 》

by
Julian W. Gardner
University of Warwick, UK
Vijay K. Varadan
Osama O. Awadelkarim
Pennsylvania State University, USA ───

 

既然是以某種的『機械結構』所構造,即使製作得很小,還是符合『物理力學』之原理。若是缺乏適當的『避震設計』,依舊免不了『振動』與『突波』的影響。所以『數據表』方才特別強調『 High shock survivability 』的乎?下面的實測結果︰

 

【不施加搖晃振動】

pi@raspberrypi ~ sudo python3 Python 3.2.3 (default, Mar  1 2013, 11:53:50)  [GCC 4.6.3] on linux2 Type "help", "copyright", "credits" or "license" for more information. >>> import time >>> from sense_hat import SenseHat >>> 感測 = SenseHat() >>> while True: ...     壓力 = 感測.get_pressure() ...     print("Pressure: %s Millibars" % 壓力) ...     time.sleep(3) ...  Pressure: 1012.38818359375 Millibars Pressure: 1012.410888671875 Millibars Pressure: 1012.41455078125 Millibars Pressure: 1012.3994140625 Millibars Pressure: 1012.368896484375 Millibars Pressure: 1012.39794921875 Millibars Pressure: 1012.411376953125 Millibars Pressure: 1012.389892578125 Millibars Pressure: 1012.4013671875 Millibars Pressure: 1012.399169921875 Millibars Pressure: 1012.37890625 Millibars Pressure: 1012.362060546875 Millibars Pressure: 1012.38330078125 Millibars Pressure: 1012.347412109375 Millibars Pressure: 1012.417724609375 Millibars Pressure: 1012.35693359375 Millibars Pressure: 1012.396484375 Millibars ^CTraceback (most recent call last):   File "<stdin>", line 4, in <module> KeyboardInterrupt >>>  </pre>    <span style="color: #808080;"><strong>【施加搖晃振動】</strong></span> <pre class="lang:sh decode:true">pi@raspberrypi ~ sudo python3
Python 3.2.3 (default, Mar  1 2013, 11:53:50) 
[GCC 4.6.3] on linux2
Type "help", "copyright", "credits" or "license" for more information.
>>> import time
>>> from sense_hat import SenseHat
>>> 感測 = SenseHat()
>>> while True:
...     壓力 = 感測.get_pressure()
...     print("Pressure: %s Millibars" % 壓力)
...     time.sleep(3)
... 
Pressure: 1012.3779296875 Millibars
Pressure: 1012.384765625 Millibars
Pressure: 1012.3642578125 Millibars
Pressure: 1012.353515625 Millibars
Pressure: 1012.378173828125 Millibars
Pressure: 1012.34765625 Millibars
Pressure: 1012.355224609375 Millibars
Pressure: 1012.345703125 Millibars
Pressure: 1012.364501953125 Millibars
Pressure: 1012.3623046875 Millibars
Pressure: 1012.36083984375 Millibars
Pressure: 1012.396484375 Millibars
Pressure: 1012.35693359375 Millibars
Pressure: 1012.397216796875 Millibars
Pressure: 1012.357177734375 Millibars
Pressure: 1012.398681640625 Millibars
Pressure: 1012.39697265625 Millibars
Pressure: 1012.390380859375 Millibars
Pressure: 1012.403564453125 Millibars
Pressure: 1012.377685546875 Millibars
Pressure: 1012.358154296875 Millibars
^CTraceback (most recent call last):
  File "<stdin>", line 4, in <module>
KeyboardInterrupt
>>> 

 

或可驗證所說矣。如是我們是否更加明白所謂『機電整合』是何事的呢?清楚知道『學科融匯』是進入未來科技世界之『通行證』的嗎??或將理解『【Sonic π】…… 』一大系列文本所談之事乎!

 

王小玉說書

清‧劉鶚‧《老殘遊記

第二回 歷山山下古帝遺蹤 明湖湖邊美人絕調

停了數分鐘時,簾子裡面出來一個姑娘,約有十六七歲,長長鴨蛋臉兒,梳了一個抓髻,戴了一副銀耳環,穿了一件藍布外褂兒,一夫 朗和斐條藍布褲子,都是黑布鑲滾的。雖是粗布衣裳,到十分潔淨。來到半桌後面右手椅子上坐下。那彈弦子的便取了弦子,錚錚鏦鏦彈起。這姑娘便立起身來,左 手取了梨花簡,夾在指頭縫裡,便丁丁當當的敲,與那弦子聲音相應。右手持了鼓捶子,凝神聽那弦子的節奏。忽羯鼓一聲,歌喉遽發,字字清脆,聲聲宛轉,如新 鶯出谷,乳燕歸巢,每句七字,每段數十句,或緩或急,忽高忽低。其中轉腔換調之處,百變不窮,覺一切歌曲腔調俱出其下,以為觀止矣。

旁 坐有兩人,其一人低聲問那人道:「此想必是白妞了罷?」其一人道:「不是。這人叫黑妞,是白妞的妹子。他的調門兒都是白妞教的,若比白妞,還不曉得差多遠 呢!他的好處人說得出,白妞的好處人說不出;他的好處人學的到,白妞的好處人學不到。你想,這幾年來,好玩耍的誰不學他們的調兒呢?就是窯子裡的姑娘,也 人人都學,只是頂多有一兩句到黑妞的地步。若白妞的好處,從沒有一個人能及他十分裡的一分的。」說著的時候,黑妞早唱完,後面去了。這時滿園子裡的人,談 心的談心,說笑的說笑。賣瓜子、落花生、山裡紅、核桃仁的,高聲喊叫著賣,滿園子裡聽來都是人聲。

正 在熱鬧哄哄的時節,只見那後臺裡,又出來了一位姑娘,年紀約十八九歲,裝束與前一個毫無分別。瓜子臉兒,白淨麵皮,相貌不過中人以上之姿,只覺得秀而不 媚,清而不寒。半低著頭出來,立在半桌後面,把梨花簡了當了幾聲。煞是奇怪,只是兩片頑鐵,到他手裡,便有了五音十二律以的。又將鼓捶子輕輕的點了兩下, 方抬起頭來,向臺下一盼。那雙眼睛,如秋水,如寒星,如寶珠,如白水銀裡頭養著兩丸黑水銀,左右一顧一看,連那坐在遠遠牆角子裡的人,都覺得王小玉看見我 了,那坐得近的更不必說。就這一眼,滿園子裡便鴉雀無聲,比皇帝出來還要靜悄得多呢,連一根針跌在地下都聽得見響!

王 小玉便啟朱脣,發皓齒,唱了幾句書兒。聲音初不甚大,只覺入耳有說不出來的妙境。五臟六腑裡,像熨斗熨過,無一處不伏貼。三萬六千個毛孔,像吃了人參果, 無一個毛孔不暢快。唱了十數句之後,漸漸的越唱越高,忽然拔了一個尖兒,像一線鋼絲拋入天際,不禁暗暗叫絕。那知他於那極高的地方,尚能迴環轉折。幾囀之 後,又高一層,接連有三四疊,節節高起。恍如由傲來峰西面攀登泰山的景象,初看傲來峰削壁千仞,以為上與天通。及至翻到傲來峰頂,才見扇子崖更在傲來峰 上。及至翻到扇子崖,又見南天門更在扇子崖上。愈翻愈險,愈險愈奇。

那 王小玉唱到極高的三四疊後,陡然一落,又極力騁其千迴百折的精神,如一條飛蛇在黃山三十六峰半中腰裡盤旋穿插。頃刻之間,周匝數遍。從此以後,愈唱愈低, 愈低愈細,那聲音漸漸的就聽不見了。滿園子的人都屏氣凝神,不敢少動。約有兩三分鐘之久,彷彿有一點聲音從地底下發出。這一出之後,忽又揚起,像放那東洋 煙火,一個彈子上天,隨化作千百道五色火光,縱橫散亂。這一聲飛起,即有無限聲音俱來並發。那彈弦子的亦全用輪指,忽大忽小,同他那聲音相和相合,有如花 塢春曉,好鳥亂鳴。耳朵忙不過來,不曉得聽那一聲的為是。正在撩亂之際,忽聽霍然一聲,人弦俱寂。這時臺下叫好之聲,轟然雷動。

停 了一會,鬧聲稍定,只聽那臺下正座上,有一個少年人,不到三十歲光景,是湖南口音,說道:「當年讀書,見古人形容歌聲的好處,有那『餘音繞梁,三日不絕』 的話,我總不懂。空中設想,餘音怎樣會得繞梁呢?又怎會三日不絕呢?及至聽了小玉先生說書,才知古人措辭之妙。每次聽他說書之後,總有好幾天耳朵裡無非都 是他的書,無論做什麼事,總不入神,反覺得『三日不絕』,這『三日』二字下得太少,還是孔子『三月不知肉味』,『三月』二字形容得透徹些!」旁邊人都說 道:「夢湘先生論得透闢極了!『於我心有戚戚焉』!」

說 著,那黑妞又上來說了一段,底下便又是白妞上場。這一段,聞旁邊人說,叫做「黑驢段」。聽了去,不過是一個士子見一個美人,騎了一個黑驢走過去的故事。將 形容那美人,先形容那黑驢怎樣怎樣好法,待鋪敘到美人的好處,不過數語,這段書也就完了。其音節全是快板,越說越快。白香山詩云:「大珠小珠落玉盤。」可 以盡之。其妙處在說得極快的時候,聽的人彷彿都趕不上聽,他卻字字清楚,無一字不送到人耳輪深處。這是他的獨到,然比著前一段卻未免遜一籌了。


詩經毛詩序

情發於聲,聲成文謂之音,治世之音安以樂,其政和;亂世之音怨以怒,其政乖;亡國之音哀以思,其民困故正得失,動天地,感鬼神,莫近於詩。先王以是經夫婦,成孝敬,厚人倫,美教化,移風俗。

風聲雨聲讀書聲雖然都是『』,但不知有幾人能詮釋『地籟』之『』;或許『誦讀聲』偶然入耳,聽之卻有『弦外之音』。終於『寰宇的振動』一分為三,成為了『自然之聲』、『言語之音』以及『動人之樂』!王小玉說書,字字清晰詞詞明白,音似行雲且聲若流水,一時雷鳴九霄之外,忽而泉湧九地之下,彼音擬樂此聲知音,相追相逐鎔鑄成了『天籟』的聲樂旋律!!

───

 

事實上,那些文本

【Sonic π】聲波之傳播原理︰振動篇

【Sonic π】聲波之傳播原理︰原理篇《一》

【Sonic π】聲波之傳播原理︰共振篇《一》

‧ …

的點點滴滴,不只是進入 MEMS 的『先修課』,更為著在分殊專業的今天,所謂『普通科學 』到底該如何講起又怎樣傳播,作點嘗試努力的吧 !!

今天是『教師節』,省思現下『教』『學』關係的『實況』,不禁令人十分悵惘無奈的啊!!到底一切的教改使『學子』的『壓力』是增是減的呢??

 

【為何壓力為零??】

# sense_hat 原始碼
sense_hat/sense_hat.py 


    def get_pressure(self):
        """
        Returns the pressure in Millibars
        """

        self._init_pressure()  # Ensure pressure sensor is initialised

# 壓力為零是初始值!
        pressure = 0
        data = self._pressure.pressureRead()
# 或代表感測器讀取有誤耶?
        if (data[0]):  # Pressure valid
            pressure = data[1]
        return pressure

    @property
    def pressure(self):
        return self.get_pressure()

 

 

 

 

 

 

 

 

 

 

勇闖新世界︰ W!o《卡夫卡村》變形祭︰感知自然‧尖端‧三

什麼是『微機電系統』 MEMS ?在此引用 State University of New  York 之 Mohammad I. Younis 先生所寫

《 MEMS Linear and Nonlinear Statics and Dynamics 》
by
Mohammad I. Younis

書中之一段說法︰

1.1 What Are MEMS and Why They Are Attractive?

The easiest way to introduce MEMS is to refer to the acronym MEMS itself and what it means. MEMS stands for micro-electro-mechanical-systems. Hence, they are devices in the “micro” scale, in which one or more of their dimensions are in the micrometer range. The “electro” part indicates that they use electric power, for example for actuation and detection, or electronics, for instance for amplifying and filtering signals and for controlling purposes. “Mechanical” means these devices rely on some sort of mechanical motion, action, or mechanism. The word “system” refers to the fact that they function, are designed, and are fabricated as integrated systems and not as individual components. In addition to these features, there are some basic aspects of MEMS that are hidden in the acronym. These can be revealed in this more formal definition of MEMS, which is the integration of mechanical elements, sensors, actuators, and electronics on a common silicon substrate through micro-fabrication technology [1].

This concise definition emphasizes important features of MEMS. The first is the fact that most MEMS are basically sensors and actuators. Examples of MEMS sensors are inertia sensors (accelerometers, gyroscopes), pressure sensors, gas and mass sensors, temperature sensors, force sensors, and humidity sensors. Almost for every physical quantity, there is a MEMS sensor that is developed or being developed to measure it. Examples of actuators are micromirrors to deflect lights in flat-screen TVs, RF switches and microrelays, microgrippers, and generic force and displacement actuators, such as thermal bimorph actuators and comb-drive electrostatic actuators. Thus, historically speaking, the early generation of MEMS researchers
has relied on sensors and actuators journals and conferences to disseminate their research on miniature devices before the introduction of specialized MEMS conferences and journals in the early 1990s. Today, several major MEMS meetings and journals still hold the words sensors, actuators, or transducers in their titles.

The second feature is that silicon represents the core material of this technology. Silicon substrates are commonly used as the platform where MEMS components are built and electrically bonded, although recently other materials, such conductive polymers have been utilized [2, 3]. The fabrication of MEMS devices usually starts with single crystal silicon wafers, which come in many standard sizes (4 in, 8 in, and 12 in). Silicon is the preferred material because of its excellent thermal and mechanical properties (small thermal expansion, high melting point, high toughness, and brittleness with no plastic behavior or hysteresis). In addition, silicon has been used
for microelectronics long before the MEMS technology. Hence, many of the well-established processes to fabricate microelectronics from silicon have been adopted directly or modified slightly for MEMS. MEMS made of silicon can be integrated easily with other electronics components, which are also made of silicon, on the same chip. Besides silicon, a number of materials are used to realize MEMS structures, such as silicon-oxide, silicon-nitride, polysilicon, gallium arsenide (GaAs), aluminum, and gold. These are grown or deposited as thin-films over the silicon substrate, which are then etched or processed by micro-fabrication techniques [4].

Another key aspect of MEMS devices is the fact that they are made through the micro-fabrication technology, which enables fabricating numerous numbers of them at the same time (batch fabrication). Many of the micro-fabrication processes, such as material deposition, evaporation, and etching, can be applied on multiple silicon wafers at the same time. Each wafer can produce hundreds of MEMS devices. This means that each fabrication batch can produce thousands of MEMS devices all at once. Of course, reaching this level of production is not trivial; micro-fabrication processes need extensive research and optimization for each step to reach stable and reliable level of production. However, once this critical stage is passed, the payoff is thousands of devices at very low cost. MEMS devices have replaced many expensive devices for fractions of the cost. For instance, the Analog Devices airbag accelerometers in cars, which today costs less than a dollar, has replaced bulkier more expensive accelerometers, which cost more than US$ 50 apiece.

Another important feature of MEMS is the fact that they are systems. This implies that the components of MEMS have to be designed during the design of the whole system. Assembly of individual MEMS components is expensive, cumbersome, and impractical [5]. Also, when designing a microsystem, its fabrication process must be designed too, otherwise the design many not be feasible or cannot be fabricated. Another implication is that system issues, such as packaging, system partitioning into components, stability, and reliability of the products, must be analyzed and taken into consideration during the design and development cycles.

麥克風

The fascination in the MEMS technology comes from their distinguished characteristics. MEMS are characterized by low cost, which is a direct consequence of the batch fabrication. They have lightweight and small size, which is desirable for compactness and convenience reasons. In addition, this has opened the gates for new possibilities of implementing MEMS in many places where large devices do not fit, such as engine of cars and inside the human body. Moreover, they consume very low power, which not only does reduce the operational cost but also enables the development of long-life and self-powered devices that can harvest the small amount of energy they need from the environment during their operation [6, 7]. Furthermore, MEMS devices have enabled many superior performances, smart functionalities, and complicated tasks that cannot be achieved in other technologies. Ultra-sensitive mass detectors, high isolation and low-insertion-loss RF switches, lab-on-a-chip bio-sensors, tiny directional microphones for hearing aids (Fig. 1.1), high-temperature pressure sensors for automobile engines (Fig. 1.2), and precise controlled liquid droplets for ink-jet printers are just few examples.

壓力感測器

───

 

再輔之以

《 Microsensors, MEMS, and Smart Devices 》

by
Julian W. Gardner
University of Warwick, UK
Vijay K. Varadan
Osama O. Awadelkarim
Pennsylvania State University, USA

書中的『分類圖解』 Classification scheme 和 MEMS 可以量測哪些『物理量』,以及『裝置構造』概要︰

 

8.4 MECHANICAL SENSORS

8.4.1 Overview

Mechanical microsensors are, perhaps, the most important class of microsensor because of both the large variety of different mechanical measurands and their successful application in mass markets, such as the automotive industry. Table 8.4 lists some 50 or so of the numerous possible mechanical measurands and covers not only static and kinematic parameters, such as displacement, velocity, and acceleration, but also physical properties of materials, such as density, hardness, and viscosity.

Figure 8.19 shows a classification scheme for mechanical microsensors together with an example of a device type.

Table 8.4 List of mechanical measurands. Adapted from Gardner (1994)

mechanical-measurands

Classification scheme

Figure 8.19 Classification scheme for mechanical microsensors. From Gardner (1994)

The most important classes of mechanical microsensors to date is a subset of only six or so and these constitute the majority of the existing market for micromechanical sensors. Thus, the main measurands of mechanical microsensors are as follows in alphabetical order:

• Acceleration/deceleration
• Displacement
• Flow rate
• Force/torque
• Position/angle
• Pressure/stress

Therefore, we describe in detail here four of the most important types of mechanical microsensors, namely,

• Pressure microsensors (Section 8.4.5)
• Microaccelerometers (Section 8.4.6)
• Microgyroscopes (Section 8.4.7)
• Flow microsensors (Section 8.4.8)

 

在這杜鵑呼嘯即將過境,或仍可借著今日『中秋佳月』之明,略窺 MEMS 之面貌的耶!!

 

 

 

 

 

 

 

 

 

勇闖新世界︰ W!o《卡夫卡村》變形祭︰感知自然‧尖端‧二

在探討『微機電系統』 MEMS 原理前,先思考

MEMS are made up of components between 1 to 100 micrometres in size (i.e. 0.001 to 0.1 mm), and MEMS devices generally range in size from 20 micrometres to a millimetre (i.e. 0.02 to 1.0 mm). They usually consist of a central unit that processes data (the microprocessor) and several components that interact with the surroundings such as microsensors.[1] At these size scales, the standard constructs of classical physics are not always useful. Because of the large surface area to volume ratio of MEMS, surface effects such as electrostatics and wetting dominate over volume effects such as inertia or thermal mass.[citation needed]

Labonachip20017-300

Microelectromechanical systems chip, sometimes called “

lab on a chip

 

所說何事。為何『經典物理』通常不合適的呢?或許『尺寸』很小時,必須要考慮『量子效應』。更重要的是主導的『作用力』以及各類『非線性』的來源與一般物理學講的『剛體』、『流體』、『連續體』…等等的巨觀『線性模型』 情況不同,通常需創造適當的『系統模型』。而且『單‧多‧巨』個體涉及的『計算複雜度』和『系統穩定性』實際上大異其趣。此時如果回顧一下

W!o 的派生‧十日談之《四》

龐加萊 Poincaré 與玻爾茲曼 Boltzmann 等人創用『相空間』phase space 來描述物理上『三體問題』的時候,催生了︰

現今的混沌理論 Chaos theory 描述『非線性』系統在一定參數條件下會發生『分岔』 bifurcation 現象,周期運動與非周期運動可能相互『糾纏』,以至於通往某種非周期又可以有序之運動理論。因此它是一種兼具『定性』與『定量』的分析之思考方法,用以探討動力系統中無法僅用『一時單一』的數據,必須用『連續整體』的數據才能加以解釋或是描述該系統之行為。

220px-Double-compound-pendulum-dimensioned.svg

Double-compound-pendulum

220px-DPLE

Double_pendulum_flips_graph

混沌』chaos 一詞源自古希臘哲學家認為宇宙起源於混亂無序的狀態,逐漸由這個混沌之初形成現今有條不紊的世界。這個混沌論說︰

一切事物的初始狀態,都只是一些看似無關的碎片,然而當此混沌過程結束之時,這些碎片終自主有序的聚合成一個整體。

左圖演示一個『雙擺』Double pendulum 的運動,系統總能量取某些數量時它的運動是混沌的。假使想要對它『數值』求解,從『數值分析』的程式設計觀點來看這個數據『敏感性』問題 ── 叫做『惡劣條件』ill condition ──,通常需要作多次多種『收斂測試』,否則到底計算出來的是什麼,可就說不清的了。有興趣物理、數學或寫程式的讀者可以參考︰

Double Pendulum

Double Pendulum Demonstration

如果問大自然『作計算』嗎?假使答『』,那該如何『作計算』的呢??比方說,人類要怎麽『模擬』一莫爾 6^{23} 個氣體分子之『運動』的呢!事實上,想深入了解『三體互動』恐怕都需要借助『計算機』的哩!!那麼『自然律』果真能與『理化計算』等同的嗎???

所以就算今天已經有了『量子電腦』,那所需之『時間』 time 與『空間』 space ,在『計算』上所用之『資料』和『結構』,依然十分重要!也許有人認為,難到不能夠依賴『統計學』的嗎?只是適用於『晴天』的『統計』,誰曉得能不能用於『雨天』的呢!!

───

 

失之豪釐,差以千里!!《中》

假使說一個系統 S 很『靈敏』 sensitive ,是講當系統的『輸入』 I 有一點『變化』 \Delta I ,系統之『輸出』 O ,產生很大的『改變』 \Delta O ,也就是說

\frac{\Delta O}{\Delta I} 的『比值』很大。

然而『靈敏度』 Sensitivity 一詞,用於不同的領域、場合,常帶著點不同的意味,遇到此詞時,避免望文生義。如果將『靈敏度』用於『量測儀器』,通常是指儀表對於『輸入變化』的『分辨能力』 ,一般用著某種 \frac{\Delta O}{\Delta I} 之『比值』來表示。

Rayleigh_criterion_plot
瑞利準則

比方說 一個光學儀器的『角分辨度』 Angular resolution

\theta \approx \sin \theta = 1.220 \frac{\lambda}{2 R}

表示要是透鏡和兩個物件之間的夾角少於 \theta ,透鏡的觀察者便無法分辨出有兩個物件。不要以為『分辨能力』愈『』,就一定是愈『』,通常顯微鏡的放大倍數『越高』,可能操作上也『越難』 。設使每個人的『視力』都能睹『秋毫之末』,怕世間『』『』的『標準』會變的吧?難想像會發明『幾 K 』的電視的哩!

『量測裝置』 S_M 是一個『物理系統』,待量測『自然萬象』 S_P 也是一個『物理系統』,彼此『交互作用』 ── 能量和物質轉化與交換 ──,得到『度量』之數據,『測知』現象系統的『狀態』。自考察『現象』之『狀態』上來講,假使從『微觀上』將之當成由『粒子系統』所構成,或許可以用『相空間』之『相圖』來觀察︰

300px-Focal_stability

430px-Pendulum_Phase_Portrait

Hamiltonian_flow_classical

340px-Limitcycle.svg

一個質量 m 物體,初始位置在 x_0,初始速度為 v_0 ,在 x 軸上運動,依據牛頓的第二運動定律,它的運動滿足一個二階微分方程式︰

\vec{F} = m \cdot \vec{a} = m \cdot \frac{d^2 x}{dt^2}

一般而言,除了一些特殊的力 \vec{F} 的形式,比方說簡諧運動之線性彈力 F = k \cdot x,微分方程式很難有『確解』,大概都得用『數值分析』的方式求解。那麼有沒有另一種運動描述辦法的呢?龐加萊和玻爾茲曼 Boltzmann 等人發展了『相空間』phase space 的想法,因為物體一旦給定了初始位置與初始速度── 一般使用動量 p = m \cdot v ──,它的運動軌跡就由牛頓的第二運動定律所確定,相空間是一個 (位置,動量) 所構成的座標系,這樣該物體的運動軌跡就畫出了相空間裡的一條線 ── 叫做相圖 phase diagram ──。一般這條曲線不會『自相交』,因為相交代表有不同的運動軌跡可以選擇,所以一旦相交會就只能是一種『週期運動』。龐加萊在研究三體問題的相圖時,卻發現只要『初始點』──  位置或動量 ──,極微小的變化,相圖就發生很大的改變,這種『敏感性』可能導致系統的『不可預測性』或是『不穩定性』。那我們的太陽系是穩定的嗎??

要是『相空間』之『相圖』發生了『相交』?也許是碰到『混沌』的吧!還是遭遇了『相變』。

相變Phase transition 是一種『臨界』現象︰

Phase transitions occur when the thermodynamic free energy of a system is non-analytic for some choice of thermodynamic variables (cf. phases). This condition generally stems from the interactions of a large number of particles in a system, and does not appear in systems that are too small. It is important to note that phase transitions can occur and are defined for non-thermodynamic systems, where temperature is not a parameter.

這個『』『解析的』,豈是『敏感』一詞了得,也許那時 S_P 系統就沒有『回頭路』的了!!

Phase-diag2.svg

A typical phase diagram. The dotted line gives the anomalous 【異常的】behavior of water.

Comparison_carbon_dioxide_water_phase_diagrams.svg

Comparison of phase diagrams of carbon dioxide (red) and water (blue) explaining their different phase transitions at 1 atmosphere

───

 

或許可為概念的先導乎?也許像感受下述現象所引發的驚訝一樣!

 

pi@raspberrypi ~ $ sudo python3
Python 3.2.3 (default, Mar  1 2013, 11:53:50) 
[GCC 4.6.3] on linux2
Type "help", "copyright", "credits" or "license" for more information.

>>> from sense_hat import SenseHat

>>> 感測器 = SenseHat()
>>> 溫度 = 感測器.get_temperature()
>>> 壓力 = 感測器.get_pressure()
>>> 濕度 = 感測器.get_humidity()

>>> print(溫度)
30.864919662475586

# 為什麼大氣壓力為零!!
>>> print(壓力)
0

>>> print(濕度)
51.61996078491211

>>> 壓力 = 感測器.get_pressure()
>>> print(壓力)
1014.302978515625

# 當真變化如是的快耶??
>>> 溫度 = 感測器.get_temperature()
>>> print(溫度)
30.955646514892578

>>> 濕度 = 感測器.get_humidity()
>>> print(濕度)
51.439903259277344

>>> 

 

 

 

 

 

 

 

 

 

 

勇闖新世界︰ W!o《卡夫卡村》變形祭︰感知自然‧尖端‧一

待船停妥,終於登上了平台。這湖心小築上圓小下方大,不知是否是象徵『地包天』的呢?突然吹來一陣霧氣,在月光照耀下,彷彿有道『彩虹』,卻看不清楚。一時霧更濃了,『邀請護照』正閃爍

 

250px-Snow_crystals    的圖案。

 

在 Mrphs 催促下,趕緊進到了小築的大廳。只見他一直向著東邊走 ,在好大一片落地景觀窗前,忽見那

 

300px-冰晕    『幻月』掛空中。

 

原本以為發生什麼危險,所以急行,此時只是驚訝『幻月』之美,難以形容。 Mrphs 開口說道︰先生『神行』不覺溫度陡降氣壓突變 。一般此時『秋雪』早來,由於湖水『鹽度』從南至北梯減,往常日湖北已經結冰,正向南擴大之中。今年氣象又變,據新數據推斷『秋雪』將延一『 旬 』旬,大約十天左右。或因為已經多次聽聞這『秋雪』之詞,總覺困惑,問曰︰什麼是『秋雪』的呢? Mrphs 說︰現今氣候只有『夏‧冬』交替,急徐不定,長短不一,其實『春‧秋』早就名存實亡了。懷念之故,用『秋雪』表示初冬之雪而已。方才『冰晶』突起,『邀請護照』上有多種『氣象』感測器 ,可以補足『 It 網』之『氣候大數據』,用本地『即時資訊』推斷天氣變化,所以知道『冰晶』將臨,很可能看得到『幻月』。當下 Mrphs 在『邀請護照』上按了按,螢幕上顯現

 

250px-Ice_crystals_on_the_box    『冰晶』影像。

 

接著講︰如果從『顯微』影像來看,考之以『形狀圖表』

 

冰晶样式

針柱狀『冰晶』,大約形成溫度是攝氏負五負六度。實在好奇如何可以『顯微觀物』的哩!因問道︰這『顯微』是什麼樣的技術呢? Mrphs 答道︰一種『微流體透鏡』的應用。它可以控制『微流體』動態形成多種『光學系統』,輔之以多類『微機電』運動感測器,足以精確定位『眼‧手』等等位置。不論『裸視』、『顯微』以及『望遠』都是一樣的運作方式。……

只覺一時茫然,即使能

Microfluidics

Microfluidics is a multidisciplinary field intersecting engineering, physics, chemistry, biochemistry, nanotechnology, and biotechnology, with practical applications to the design of systems in which low volumes of fluids are processed to achieve multiplexing, automation, and high-throughput screening.[1] Microfluidics emerged in the beginning of the 1980s and is used in the development of inkjet printheads, DNA chips, lab-on-a-chip technology, micro-propulsion, and micro-thermal technologies. It deals with the behavior, precise control and manipulation of fluids that are geometrically constrained to a small, typically sub-millimeter, scale. Typically, micro means one of the following features:

  • small volumes (µL, nL, pL, fL)
  • small size
  • low energy consumption
  • effects of the micro domain

Typically fluids are moved, mixed, separated or otherwise processed. Numerous applications employ passive fluid control techniques like capillary forces. In some applications external actuation means are additionally used for a directed transport of the media. Examples are rotary drives applying centrifugal forces for the fluid transport on the passive chips. Active microfluidics refers to the defined manipulation of the working fluid by active (micro) components such as micropumps or micro valves. Micro pumps supply fluids in a continuous manner or are used for dosing. Micro valves determine the flow direction or the mode of movement of pumped liquids. Often processes which are normally carried out in a lab are miniaturized on a single chip in order to enhance efficiency and mobility as well as reducing sample and reagent volumes.

───

,又能

Optofluidics

Optofluidics is a research and technology area that combines the advantages of microfluidics and optics. Applications of the technology include displays, biosensors, lab-on-chip devices, lenses, and molecular imaging tools and energy.

History

The idea of fluid-optical devices can be traced back at least as far as the 18th century, when spinning pools of mercury were proposed (and eventually developed) as liquid mirror telescopes. In the 20th century new technologies such as dye lasers and liquid core waveguides were developed that took advantage of the tunability and physical adaptability that liquids provided to these newly emerging photonic systems. The field of optofluidics formally began to emerge in the mid-2000s as the fields of microfluidics and nanophotonics were maturing and researchers began to look for synergies between these two areas.[1] One of the primary applications of the field is for lab-on-a-chip and biophotonic products.[2][3][4]

 

有這麼高的科技,在那遙遠的未來。若不再有『美麗地球』,一切到底所為何來的耶!!??

 

 

 

 

 

 

 

 

 

勇闖新世界︰ W!o《卡夫卡村》變形祭︰感知自然‧湖心小築

眼前一座圓形的平台在望,中央有個圓頂式建築物看來最高。此時東西分界線歷歷在目, Mrphs 說道︰湖心小築將至。基址的平台是圓的,徑長千『 步 』步。此處的『 步 』是長度計量單位 ,大約等於貴處的『三十公分』 。此湖心小築呈方形,廣三百步,建在台中央 。台面上只有兩層,水面下有百層,總高亦千步。除去南北渡頭外,周圓都有房舍,連同築頂之觀星圓台,全部都隸屬『天文‧氣象』研究所。湖心小築入口大廳在第一層,向下五十層是『人文‧科技』大學堂,再下五十層是『地理‧海洋』調查室。因為此築位於東西線交界之處,由於南北水位斷差有三百步,所以『地理‧海洋』調查室實有大半樓層,一邊面湖,一邊深入土中,形成了理想地文研究環境。心想︰分明偌大的建築,怎麼會叫湖心小築的呢? Mrphs 接著又講︰說來當初此地谷民集資集力建造這所『大學堂』是為著感謝 M♪o 的貢獻,誰知她喜歡與小朋友為伍不願離開『小學堂』。於是在 M♪o 的建議下,成了『盤谷大學』,全體谷民的大學。據聞這『湖心小築』之名,也是那時定的。說是取象於『尖』,上『小』下『大』之謂。曾有人問過  M♪o 這事,她只莞爾笑說︰地山謙和尖不尖能有什麼關係?謹慎不要山地剝就好了 !事實上,至今還有人繼續『徇名責實』的哩。現今許多『尖端』研究,谷民僅需提出申請,只要不違背『科技護生』之旨,可在此自由進行 。那『邀請護照』正是科研的成果之一。……

一時聽的恍神,忽想起物理大師『費因曼』的創見

There’s Plenty of Room at the Bottom

There’s Plenty of Room at the Bottom” was a lecture given by physicist Richard Feynman at an American Physical Society meeting at Caltech on December 29, 1959.[1] Feynman considered the possibility of direct manipulation of individual atoms as a more powerful form of synthetic chemistry than those used at the time. The talk went unnoticed and it didn’t inspire the conceptual beginnings of the field. In the 1990s it was rediscovered and publicised as a seminal event in the field, probably to boost the history of nanotechnology with Feynman’s reputation.

Conception

Feynman considered a number of interesting ramifications of a general ability to manipulate matter on an atomic scale. He was particularly interested in the possibilities of denser computer circuitry, and microscopes that could see things much smaller than is possible with scanning electron microscopes. These ideas were later realized by the use of the scanning tunneling microscope, the atomic force microscope and other examples of scanning probe microscopy and storage systems such as Millipede, created by researchers at IBM.

Feynman also suggested that it should be possible, in principle, to make nanoscale machines that “arrange the atoms the way we want”, and do chemical synthesis by mechanical manipulation.

He also presented the “weird possibility” of “swallowing the doctor,” an idea that he credited in the essay to his friend and graduate student Albert Hibbs. This concept involved building a tiny, swallowable surgical robot by developing a set of one-quarter-scale manipulator hands slaved to the operator’s hands to build one-quarter scale machine tools analogous to those found in any machine shop. This set of small tools would then be used by the small hands to build and operate ten sets of one-sixteenth-scale hands and tools, and so forth, culminating in perhaps a billion tiny factories to achieve massively parallel operations. He uses the analogy of a pantograph as a way of scaling down items. This idea was anticipated in part, down to the microscale, by science fiction author Robert A. Heinlein in his 1942 story Waldo.[2][3]

As the sizes got smaller, one would have to redesign some tools, because the relative strength of various forces would change. Although gravity would become unimportant, surface tension would become more important, Van der Waals attraction would become important, etc. Feynman mentioned these scaling issues during his talk. Nobody has yet attempted to implement this thought experiment, although it has been noted that some types of biological enzymes and enzyme complexes (especially ribosomes) function chemically in a way close to Feynman’s vision.

───

 

,不知到底如何想出!

想來學問之『山』,一『山』還比一『山』高的吧!!

 

 

 

 

 

 

 

 

 

 

輕。鬆。學。部落客