每日彙整: 2018-08-24

樹莓派、樹莓派之學習、樹莓派之教育

STEM 隨筆︰鬼月談化學︰☵ 陷 《變化》

『卜筮』是為『決疑』，既然『無疑』又何需『卜筮』的呢？孔子既卜得『賁』卦，又為什麼以為『不好』的呢？如果看《易經》的《十翼》，或可知其一二

彖曰：賁，亨﹔柔來而文剛，故亨。分剛上而文柔，故小利有攸往。天文也﹔文明以止，人文也。觀乎天文，以察時變﹔觀乎人文，以化成天下。

象曰：山下有火，賁﹔君子以明庶政，無敢折獄。

顯然像『子貢』說的是個『吉卦』的吧！『賁』是『文采』，想『孔老夫子』周遊列國一無所成，正感嘆著『無力於』這個『黑白不分』的時代，偏偏卻得到這麼個『紋過飾非』的現實『象徵』，他老先生當然『不高興』的啦！想必是占卜『所求不得』的吧！！

就像《觀水》一文中講古人喜歡『論水』講『智者樂水』，那麼『易經』中的『坎為水』為什麼又是『坎陷』與『坎險』的意思的呢？或許『智』和『險』本相反相成，就像是『善泳者死於水』的告誡一般，『水之潤下』的『特性』使它容易遇着『坑‧洞』等等『陷阱』，因此此卦特別用『習坎』為名強調需要一再的『練習』以及『謹慎』之意的吧！！

漢代有兩位『京房』，都研究『易經』，也都是『太守』，一是

『齊郡太守』之京房：漢昭帝時為太中大夫、齊郡太守，治易學，師從菑川人『楊何』。有弟子『梁丘賀』。

，另一是

『郎、魏郡太守』之京房︰字君明，東郡頓丘人。西漢學者漢元帝時官員。本 姓李，因其愛好吹奏音律，自定為京氏，羌笛原本有三個音孔，京房改進後成了多一個，音孔定為商聲，從而使它能奏全宮、商、角、徵、羽五聲。漢元帝時為郎、 魏郡太守。治易學，師從梁人『焦延壽』，詳於災異，開創了京氏易學，有《京氏易傳》存世。焦延壽曾憂慮說︰『得我道以亡身者，京生也。』漢元帝初元四年，西羌叛亂，又有日蝕。漢元帝召見他時，京房宣稱：『古帝王以功舉賢，則萬化成，瑞應著；末世以毀譽取人，故功業廢而致災異。宜令百官各試其功，災異可息。』又提出《考功課吏法》 。當時宦官石顯擔任中書令，誣陷其誹謗朝政，歸惡天子，元帝將京房下獄，死獄中。

這位『京房』青出於藍，以易經的《說卦傳‧第十章》之『乾坤生六子』創造了『易經‧象數派』之『八宮卦』，之後宋代著名的『安樂先生‧邵康節』用於『梅花易數』，今日『命理術數』所稱『世應』，所取干支『五行生剋』，從之而出，果真耶其是『無的放矢』的嗎？卻又因『以功舉賢』得罪『當道宦官』以『取死』，若是果非耶『不可前知』的呢？？於此僅列出『習坎』之『京房八宮卦』的『彖‧象對照』以饗讀者吧！

甲骨文習
易經‧坎卦
坎：習坎，有孚，維心亨，行有尚。

彖曰：習坎，重險也。 水流而不盈，行險而不失其信。 維心亨，乃以剛中也。 行有尚，往有功也。 天險不可升也，地險山川丘陵也，王公設險以守其國，坎之時用大矣哉！
象曰：水洊至，習坎﹔君子以常德行，習教事。

初六：習坎，入于坎窞，凶。
象曰：習坎入坎，失道凶也。

 

 

 

九二：坎有險，求小得。
象曰：求小得，未出中也。

 

 

 

六三：來之坎坎，險且枕，入于坎窞，勿用。
象曰：來之坎坎，終無功也。

 

 

六四：樽酒簋貳，用缶，納約自牖，終無咎。
象曰：樽酒簋貳，剛柔際也。

 

 

 

九五：坎不盈，只既平，無咎。
象曰：坎不盈，中未大也。

 

 

 

 

 

 

 

上六：係用徽纆，置于叢棘，三歲不得，凶。
象曰：上六失道，凶三歲也。

幼鳥在巢裡振動翅膀練習飛行。

《說文解字》：習，數飛也。从羽，从白。凡習之屬皆从習。

 

 

 

 

 

 

一世‧水澤節 ☵ ☱

彖曰：節，亨，剛柔分，而剛得中。苦節不可貞，其道窮也。說以行險，當位以節，中正以通。 天地節而四時成，節以制度，不傷財，不害民。
象曰：澤上有水，節﹔君子以制數度，議德行。

二世‧水雷屯 ☵ ☳

彖曰：屯，剛柔始交而難生，動乎險中，大亨貞。雷雨之動滿盈，天造草昧，宜建侯而不寧。
象曰：云，雷，屯﹔君子以經綸。

三世‧水火既濟 ☵ ☲

彖曰：既濟，亨，小者亨也。利貞，剛柔正而位當也。 初吉，柔得中也。終止則亂，其道窮也。
象曰：水在火上，既濟﹔君子以思患而預防之。

四世‧澤火革 ☱ ☲

彖曰：革，水火相息，二女同居，其志不相得，曰革。己日乃孚﹔革而信也。 文明以說，大亨以正，革而當，其悔乃亡。天地革而四時成，湯武革命，順乎天而應乎人，革之時義大矣哉！
象曰：澤中有火，革﹔君子以治歷明時。

五世‧雷火豐 ☳ ☲

彖曰：丰，大也。 明以動，故丰。王假之，尚大也。 勿憂宜日中，宜照天下也。日中則昃，月盈則食，天地盈虛，與時消息，而況於人乎？況於鬼神乎？
象曰：雷電皆至，丰﹔君子以折獄致刑。

遊魂‧地火明夷 ☷ ☲

彖曰：明入地中，明夷。 內文明而外柔順，以蒙大難，文王以之。 利艱貞，晦其明也，內難而能正其志，箕子以之。
象曰：明入地中，明夷﹔君子以蒞眾，用晦而明。

歸魂‧地水師 ☷ ☵

彖曰：師，眾也，貞正也，能以眾正，可以王矣。 剛中而應，行險而順，以此毒天下，而民從之，吉又何咎矣。
象曰：地中有水，師﹔君子以容民畜眾。

─── 《水的生命！！下》

 

俗話說︰『謠言』止於『智者』。既有所『止』，焉無所『始』乎 ？ 有曰︰『造假』出自『聰明人』也！

想當初練習『化學動力學』

Chemical kinetics

Chemical kinetics, also known as reaction kinetics, is the study of rates of chemical processes. Chemical kinetics includes investigations of how different experimental conditions can influence the speed of a chemical reaction and yield information about thereaction’s mechanism and transition states, as well as the construction of mathematical models that can describe the characteristics of a chemical reaction.

 

讀其簡短『歷史』

History

In 1864, Peter Waage and Cato Guldberg pioneered the development of chemical kinetics by formulating the law of mass action, which states that the speed of a chemical reaction is proportional to the quantity of the reacting substances.[1][2][3]

Van ‘t Hoff studied chemical dynamics and published in 1884 his famous “Etudes de dynamique chimique”.[4] In 1901 he was awarded by the first Nobel Prize in Chemistry “in recognition of the extraordinary services he has rendered by the discovery of the laws of chemical dynamics and osmotic pressure in solutions”.[5] After van ‘t Hoff, chemical kinetics deals with the experimental determination of reaction rates from which rate laws and rate constants are derived. Relatively simple rate laws exist for zero order reactions (for which reaction rates are independent of concentration), first order reactions, and second order reactions, and can be derived for others. Elementary reactions follow the law of mass action, but the rate law of stepwise reactions has to be derived by combining the rate laws of the various elementary steps, and can become rather complex. In consecutive reactions, the rate-determining step often determines the kinetics. In consecutive first order reactions, a steady state approximation can simplify the rate law. The activation energyfor a reaction is experimentally determined through the Arrhenius equation and the Eyring equation. The main factors that influence the reaction rate include: the physical state of the reactants, the concentrations of the reactants, the temperature at which the reaction occurs, and whether or not any catalysts are present in the reaction.

Gorban and Yablonsky have suggested that the history of chemical dynamics can be divided into three eras.[6] The first is the van ‘t Hoff wave searching for the general laws of chemical reactions and relating kinetics to thermodynamics. The second may be called theSemenov—Hinshelwood wave with emphasis on reaction mechanisms, especially for chain reactions. The third is associated with Aris and the detailed mathematical description of chemical reaction networks.

 

數過『影響因素』之數

Factors affecting reaction rate

Nature of the reactants

The reaction rate varies depending upon what substances are reacting. Acid/base reactions, the formation of salts, and ion exchange are usually fast reactions. When covalent bond formation takes place between the molecules and when large molecules are formed, the reactions tend to be slower.

The nature and strength of bonds in reactant molecules greatly influence the rate of their transformation into products.

Physical state

The physical state (solid, liquid, or gas) of a reactant is also an important factor of the rate of change. When reactants are in the same phase, as in aqueous solution, thermal motion brings them into contact. However, when they are in different phases, the reaction is limited to the interface between the reactants. Reaction can occur only at their area of contact; in the case of a liquid and a gas, at the surface of the liquid. Vigorous shaking and stirring may be needed to bring the reaction to completion. This means that the more finely divided a solid or liquid reactant the greater its surface area per unit volume and the more contact it with the other reactant, thus the faster the reaction. To make an analogy, for example, when one starts a fire, one uses wood chips and small branches — one does not start with large logs right away. In organic chemistry, on water reactions are the exception to the rule that homogeneous reactions take place faster than heterogeneous reactions.

Surface area of solids

In a solid, only those particles that are at the surface can be involved in a reaction. Crushing a solid into smaller parts means that more particles are present at the surface, and the frequency of collisions between these and reactant particles increases, and so reaction occurs more rapidly. For example, Sherbet (powder) is a mixture of very fine powder of malic acid (a weak organic acid) and sodium hydrogen carbonate. On contact with the saliva in the mouth, these chemicals quickly dissolve and react, releasing carbon dioxide and providing for the fizzy sensation. Also, fireworks manufacturers modify the surface area of solid reactants to control the rate at which the fuels in fireworks are oxidised, using this to create different effects. For example, finely divided aluminium confined in a shell explodes violently. If larger pieces of aluminium are used, the reaction is slower and sparks are seen as pieces of burning metal are ejected.

Concentration

Main article: Rate equation

 

The reactions are due to collisions of reactant species. The frequency with which the molecules or ions collide depends upon their concentrations. The more crowded the molecules are, the more likely they are to collide and react with one another. Thus, an increase in the concentrations of the reactants will usually result in the corresponding increase in the reaction rate, while a decrease in the concentrations will usually have a reverse effect. For example, combustion will occur more rapidly in pure oxygen than in air (21% oxygen).

The rate equation shows the detailed dependence of the reaction rate on the concentrations of reactants and other species present. Different mathematical forms are possible depending on the reaction mechanism. The actual rate equation for a given reaction is determined experimentally and provides information about the reaction mechanism. The mathematical expression of the rate equation is often given by

rate = k [A]x[B]y

Here ‘x’ and ‘y’ are constants for each reactant, while [A] and [B] are molar concentrations of reactants. Also ‘k’ is the reaction rate constant which can only be determined experimentally.

Temperature

Main article: Arrhenius equation

 

Temperature usually has a major effect on the rate of a chemical reaction. Molecules at a higher temperature have more thermal energy. Although collision frequency is greater at higher temperatures, this alone contributes only a very small proportion to the increase in rate of reaction. Much more important is the fact that the proportion of reactant molecules with sufficient energy to react (energy greater than activation energy: E > Ea) is significantly higher and is explained in detail by the Maxwell–Boltzmann distribution of molecular energies.

The ‘rule of thumb’ that the rate of chemical reactions doubles for every 10 °C temperature rise is a common misconception. This may have been generalized from the special case of biological systems, where the α (temperature coefficient) is often between 1.5 and 2.5.

A reaction’s kinetics can also be studied with a temperature jump approach. This involves using a sharp rise in temperature and observing the relaxation time of the return to equilibrium. A particularly useful form of temperature jump apparatus is a shock tube, which can rapidly jump a gas’s temperature by more than 1000 degrees.

Catalysts

Main article: Catalysis

Generic potential energy diagram showing the effect of a catalyst in a hypothetical endothermic chemical reaction. The presence of the catalyst opens a different reaction pathway (shown in red) with a lower activation energy. The final result and the overall thermodynamics are the same.

A catalyst is a substance that alters the rate of a chemical reaction but remains chemically unchanged afterwards. The catalyst increases the rate of the reaction by providing a different reaction mechanism to occur with a loweractivation energy. In autocatalysis a reaction product is itself a catalyst for that reaction leading to positive feedback. Proteins that act as catalysts in biochemical reactions are called enzymes. Michaelis–Menten kinetics describe the rate of enzyme mediated reactions. A catalyst does not affect the position of the equilibrium, as the catalyst speeds up the backward and forward reactions equally.

In certain organic molecules, specific substituents can have an influence on reaction rate in neighbouring group participation.[citation needed]

Pressure

Increasing the pressure in a gaseous reaction will increase the number of collisions between reactants, increasing the rate of reaction. This is because the activity of a gas is directly proportional to the partial pressure of the gas. This is similar to the effect of increasing the concentration of a solution.

In addition to this straightforward mass-action effect, the rate coefficients themselves can change due to pressure. The rate coefficients and products of many high-temperature gas-phase reactions change if an inert gas is added to the mixture; variations on this effect are called fall-off and chemical activation. These phenomena are due to exothermic or endothermic reactions occurring faster than heat transfer, causing the reacting molecules to have non-thermal energy distributions (non-Boltzmann distribution). Increasing the pressure increases the heat transfer rate between the reacting molecules and the rest of the system, reducing this effect.

Condensed-phase rate coefficients can also be affected by (very high) pressure; this is a completely different effect than fall-off or chemical-activation. It is often studied using diamond anvils.

A reaction’s kinetics can also be studied with a pressure jump approach. This involves making fast changes in pressure and observing the relaxation time of the return to equilibrium.

Presence of Light

Light provides necessary activation energy to the starting materials, therefore, most of the reactions becomes faster in the presence of light

 

讚嘆『生生不息』造化，果然『不可思議』哩！！

能在『非線性』『平衡』

Equilibrium

While chemical kinetics is concerned with the rate of a chemical reaction, thermodynamics determines the extent to which reactions occur. In a reversible reaction, chemical equilibrium is reached when the rates of the forward and reverse reactions are equal [the principle of dynamic equilibrium ] and the concentrations of the reactants and Products no longer change. This is demonstrated by, for example, the Haber–Bosch process for combining nitrogen and hydrogen to produce ammonia. Chemical clock reactions such as the Belousov–Zhabotinsky reaction demonstrate that component concentrations can oscillate for a long time before finally attaining the equilibrium.

 

中，游刃有餘耶？？

故爾今日『後話先講』

Chemical kinetics

In chemistry one is often interested in how fast a chemical process proceeds. Chemical reactions (when viewed as single events on a molecular scale) are probabilitic. However, most reactive systems of interest involve very large numbers of molecules (a few grams of a simple substance containts on the order of {10}^{23} molecules. The sheer number allows us to describe this inherently stochastic process deterministically.

Law of mass action

In order to describe chemical reactions as as system of ODEs in terms of concentrations (cici) and time (tt), one can use the law of mass action:

\frac{dc_i}{dt} = \sum_j S_{ij} r_j

where r_j is given by:

r_j = k_j\prod_l c_l^{R_{jl}}

and S is a matrix with the overall net stoichiometric coefficients (positive for net production, negative for net consumption), and R is a matrix with the multiplicities of each reactant for each equation.

Example: Nitrosylbromide

We will now look at the following (bi-directional) chemical reaction:

\mathrm{2\,NO + Br_2 \leftrightarrow 2\,NOBr}

which describes the equilibrium between nitrogen monoxide (NO) and bromine (Br22) and nitrosyl bromide (NOBr). It can be represented as a set of two uni-directional reactions (forward and backward):

\mathrm{2\,NO + Br_2 \overset{k_f}{\rightarrow} 2\,NOBr} \\ \mathrm{2\,NOBr \overset{k_b}{\rightarrow} 2\,NO + Br_2}

The law of mass action tells us that the rate of the first process (forward) is proportional to the concentration Br_2 and the square of the concentration of NO. The rate of the second reaction (the backward process) is in analogy proportional to the square of the concentration of NOBr. Using the proportionality constants k_f and k_b we can formulate our system of nonlinear ordinary differential equations as follows:

\frac{dc_1}{dt} = 2(k_b c_3^2 - k_f c_2 c_1^2) \\ \frac{dc_2}{dt} = k_b c_3^2 - k_f c_2 c_1^2 \\ \frac{dc_3}{dt} = 2(k_f c_2 c_1^2 - k_b c_3^2)

where we have denoted the concentration of NO, Br_2, NOBr with c_1, c_2, c_3 respectively.
This ODE system corresponds to the following two matrices:

S = \begin{bmatrix} -2 & 2 \\ -1 & 1 \\ 2 & -2 \end{bmatrix}

R = \begin{bmatrix} 2 & 1 & 0 \\ 0 & 0 & 2 \end{bmatrix}

 

 

方便『有所準備』勒！！？？

/pyneqsys

Solve symbolically defined systems of non-linear equations numerically.

pyneqsys

Build status Build status on CircleCI Build status on Travis-CI PyPI version Python version DOI License file coverage

pyneqsys provides a convenience class for representing and solving non-linear equation systems from symbolic expressions (provided e.g. with the help of SymPy).

The numerical root finding is perfomed using either:

In addition to offering a unified interface to different solvers, pyneqsys can also derive the Jacobian analytically (when usingpyneqsys.SymbolicSys). This is useful since doing so manually is widely recognized as both tedious and error prone.

The symbolic representation is usually in the form of SymPy expressions, but the user may choose another symbolic back-end (seesym).

In addition to deriving the Jacobian analytically the symbolic representation can for example apply row-reduce. This is usful for when you have a overdetermined system ( formed from e.g. applying conservation laws) and want to solve the system by root-finding rather than using a least-square optimization of e.g. Levenberg-Marquardt style.

Last, but not the least having a symbolic representation of your system of equations allows you to generate publication quality latex representations of your equations (through SymPy’s latex printer) from a single source‒no more error prone hand-rewriting of the same equations in another format for presentation!

Documentation

Autogenerated API documentation for latest stable release is found here: https://bjodah.github.io/pyneqsys/latest (and the development version for the current master branch is found here: http://hera.physchem.kth.se/~pyneqsys/branches/master/html).

※ 註︰ 安裝

sudo apt-get install libsundials-*
sudo pip3 install pykinsol
sudo pip3 install pyneqsys