內容請看下面視頻
https://www.youtube.com/watch?v=qoS5zOrcMjQ
2023年5月10日 星期三
2023年4月11日 星期二
2022年3月5日 星期六
全民檢測成效成疑，尷尬的數學真相
近日全民檢測新冠病毒甚囂塵上。大部人誤會全民檢測後就可截斷傳播鍊，大家重回正常生活。但從統計學角度這只是一廂情願而已。
下為 EU 對 Rapid Antigen Test 的要求：
[Sensitivity and specificity of nucleic acid testing in close contacts of COVID-19 cases in Guangzhou] 核酸測試靈敏度研究
以下為試劑在不同靈敏度及總體感染量下的估計誤測數及預計隔離人數：
1.
以有感染為陽性。
Sensitivity 90%，即有10%陽性被測不出，被錯認為陰性。Specificity 98%，即有2%陰性被錯認為陽性。
假設本地受感染率為15%，以700萬人計，真陽性應為105萬人。
無感染為595萬人。
陽性但驗不出的有10萬5千人。受感染又驗出陽性的有94萬5千人。
無染疫但卻被劃成陽性的有11萬9千人。
故此陽性準確率是94.5/(94.5+11.9)=88.82%
陰性準確率為583.1/(583.1+10.5)=98.23%
如凡驗出陽性要隔離，則隔離人數為 (94.5+11.9)=106.4萬人。
如只能提供10萬個隔離位則有88.7萬真陽性的人要在家隔離。
另外亦有10.5萬陽性的人走漏進入社區。
2.
以有感染為陽性。
Sensitivity 90%，即有10%陽性被測不出，被錯認為陰性。Specificity 98%，即有2%陰性被錯認為陽性。
假設本地受感染率為10%，以700萬人計，真陽性應為70萬人。
無感染為617.4萬人。
陽性但驗不出的有7萬人。受感染又驗出陽性的有63萬人。
無染疫但卻被劃成陽性的有12萬6千人。
故此陽性準確率是63/(63+12.6)=83.33%
陰性準確率為617.4/(6617.4+7)=98.87%
如凡驗出陽性要隔離，則隔離人數為 (63+12.6)=75.6萬人。
如只能提供10萬個隔離位則有54.7萬真陽性的人要在家隔離。
另外亦有7萬陽性的人走漏進入社區。
3.
以有感染為陽性。
Sensitivity 95%，即有5%陽性被測不出，被錯認為陰性。Specificity 98%，即有2%陰性被錯認為陽性。
假設本地受感染率為10%，以700萬人計，真陽性應為70萬人。
無感染為630萬人。
陽性但驗不出的有3.5萬人。受感染又驗出陽性的有66.5萬人。
無染疫但卻被劃成陽性的有12萬6千人。
故此陽性準確率是66.5/(66.5+12.6)=84.07%
陰性準確率為617.4/(617.4+3.5)=99.44%
如凡驗出陽性要隔離，則隔離人數為 (66.5+12.6)=79.1萬人。
如只能提供10萬個隔離位則有58.1萬真陽性的人要在家隔離。
另外亦有3.5萬陽性的人走漏進入社區。
4.
以有感染為陽性。
Sensitivity 97%，即有3%陽性被測不出，被錯認為陰性。Specificity 98%，即有2%陰性被錯認為陽性。
假設本地受感染率為10%，以700萬人計，真陽性應為70萬人。
無感染為630萬人。
陽性但驗不出的有2.1萬人。受感染又驗出陽性的有67.9萬人。
無染疫但卻被劃成陽性的有12萬6千人。
故此陽性準確率是67.9/(67.9+12.6)=84.35%
陰性準確率為617.4/(617.4+2.1)=99.66%
如凡驗出陽性要隔離，則隔離人數為 (67.9+12.6)=80.5萬人。
如只能提供10萬個隔離位則有59.5萬真陽性的人要在家隔離。
另外亦有2.1萬假陰性真陽性的人走漏進入社區。
5.
以有感染為陽性。（以核酸測試最高 Sensitivity算）
Sensitivity 99%，即有1%陽性被測不出，被錯認為陰性。Specificity 98%，即有2%陰性被錯認為陽性。
假設本地受感染率為10%，以700萬人計，真陽性應為70萬人。
無感染為630萬人。
陽性但驗不出的有0.7萬人。受感染又驗出陽性的有69.3萬人。
無染疫但卻被劃成陽性的有12萬6千人。
故此陽性準確率是69.3/(69.3+12.6)=84.62%
陰性準確率為617.4/(617.4+0.7)=99.89%
如凡驗出陽性要隔離，則隔離人數為 (69.3+12.6)=81.9萬人。
如只能提供10萬個隔離位則有60.84萬真陽性的人要在家隔離。
另外亦有0.7萬假陰性真陽性的人走漏進入社區。
6.
下為最樂觀估計。
目前尚有277萬人一針未打。假定只有一針未打才會染疫。
以有感染為陽性。
Sensitivity 97%，即有3%陽性被測不出，被錯認為陰性。Specificity 98%，即有2%陰性被錯認為陽性。
假設此群組受感染率為15%，以27萬人計，真陽性應為41.55萬人。
無感染為235.45萬人。
陽性但驗不出的有1.25萬人。受感染又驗出陽性的有40.3萬人。
無染疫但卻被劃成陽性的有4萬7千人。
故此陽性準確率是89.54%
陰性準確率為99.46%
如凡驗出陽性要隔離，則隔離人數為 45萬人。
如只能提供10萬個隔離位則有31.35萬真陽性的人要在家隔離。
另外亦有1.25萬假陰性真陽性的人走漏進入社區。
以上只是一次全檢的推算。
要注意的是在家隔離的人因個人及緊密接觸者皆會著重防疫故在轉陰前傳染他人機會是較低。
反為假陰性的數萬人會在正常社交中較大機會傳染他人。
By WK Leung MHKIE, RPE, CEng, MIMarEST, CMarEng
All Rights Reserved©2022 fengshuileung
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2021年6月28日 星期一
Triplet control prevents ‘lasing death’ in perovskite lasers
https://physicsworld.com/a/triplet-control-prevents-lasing-death-in-perovskite-lasers/
On paper, perovskites make great building blocks for lasers. In their quasi-two-dimensional form, these organic–inorganic materials exhibit tunable colour and excellent stability. The fact that they can fabricated from low-cost starting components in simple solution-based processes makes them attractive for manufacturers, too. There’s just one tiny flaw: perovskite-based lasers abruptly stop working after only a few minutes of constant operation at room temperature. Now, however, a team of researchers in China and Japan say they have overcome this so-called “lasing death” by suppressing long-lived energetic states known as triplet excitons.
Both 2D and quasi-2D perovskites are promising alternatives to silicon in optoelectronics devices. While 2D perovskites are made up of stacked sheets of alternating organic and inorganic layers, their quasi-2D variants contain small regions in which organic and inorganic materials alternate in all directions (as is the case in their 3D counterparts). The quasi-2D versions also contain two different types of organic materials.
In organic semiconductors such as those that make up quasi-2D perovskites, charge carriers – electrons and holes – come together to form an energetic state called an exciton. This entity may exist in a so-called singlet state (which has no net spin because the contributing electron spins point in opposite directions) or in a triplet state (in which the spins point in the same direction). In both cases, the energy in the exciton can then be released as light via a process known as radiative recombination. Triplets generally have a lower energy than singlets, however, and emit hardly any light.
Long triplet lifetimes
Recently, researchers led by Chuanjiang Qin of the Chinese Academy of Sciences and Chihaya Adachi at Kyushu University in Japan found evidence that triplet excitons have lifetimes of nearly a microsecond in these materials. These long lifetimes led them to focus on these excitons as a possible cause of lasing death.
As well as emitting very little or no light, triplet states also tend to interact with light-emitting singlets in a way that causes both to lose their energy without producing light, Qin explains. Eliminating any triplets in perovskites would therefore prevent interference with lasing.
In their latest work, the researchers studied FAPbBr3-based (where FA is formamidinium) quasi-2D perovskites with two different organic cations, phenylethylammonium bromide (PEABr) and 1-naphthylmethylamine bromide (NMABr). The PEABr-based perovskite contains an organic cation with high triplet energy, and the NMABr-based perovskite has an organic cation with low triplet energy.
Holding triplets in a low energy state
To eliminate triplets in these quasi-2D perovskites, the researchers incorporated an organic layer into the materials, which confines the triplets to a low-energy state. Since the excitons want to move to lower energies, the long-lived triplet excitons transfer from the active (that is, light-emitting) portion of the perovskites to the organic layer, they explain. This reduces light losses and allows for lasing under constant optical excitation (also known as optically pumped continuous-wave, or CW lasing) without interruption.
Qin, Adachi and colleagues also discovered that they could make their material lase continuously simply by placing it in air. This is because oxygen can destroy triplets – a result that further suggests that light losses caused by triplets may indeed be the culprits in lasing death.
Unchanged lasing intensity
The researchers quantified their material’s performance by measuring the amplified spontaneous emission (ASE) intensity of the two films as they were optically powered. They found that the ASE, or lasing, remained virtually unchanged after an hour at room temperature in air with a relative humidity of 55%. The lasing spectrum also maintained its narrowness (full width at half maximum) without shifting. The team stress that these measurements were taken without the films being encapsulated in glass, and without a protective layer over their tops, as was the case in previous ASE stability measurements of 3D perovskites such as MAPbBr3.
According to the researchers, the excellent stability of their material comes from the protection provided by the larger cations on its surface. “We have demonstrated the key role of triplets in the lasing process of these types of perovskites and the importance of managing triplets to achieve continuous lasing,” Adachi states in a Kyushu University press release. “These new findings will pave the way for the future development of a new class of electrically operated lasers based on perovskites that are low cost and easily fabricated.”
2021年6月27日 星期日
2021年5月19日 星期三
Why do Indonesians prefer to have a vacation to Singapore, where the daily price is more expensive than Australia?
Why do Indonesians prefer to have a vacation to Singapore, where the daily price is more expensive than Australia?
- Airfare cost to Singapore is cheaper than to Australia. Flight to Singapore can cost as low as IDR 800,000 roundtrip (About USD 75)
- It only takes 1 hour flight to reach Singapore while flight from Jakarta to Sydney takes 6 hours
- Indonesians don't need visa to visit Singapore, while it cost $100 to have Australia's tourist visa
- Singapore is small so that tourist can explore it in 1 till 3 days. This can be an efficient option for Indonesians since leave days in Indonesia is really short
- Public transportation in Singapore is well connected and quite affordable, making it easier to be explore comparing to big cities in OZ like Melbourne, Sydney, and Perth
- Singapore has great culinary scene with great variety of halal foods, which suitable with Muslim travelers from Indonesia
- Few Indonesians have relatives in Singapore and many upper class Indonesians have apartment in Singapore
- Malay language are still used in Singapore, making Indonesians that don't understand English more comfortable when exploring Singapore
- Singapore climate is same as Indonesia, so that Indonesian tourists don't need special clothes to be prepared
- Sometimes gadgets/electronic appliances prices in Singapore cheaper than in Indonesia. The specification often more advance. Therefore many Indonesians go there to buy that stuff
2021年5月16日 星期日
F = ma & Ohm's law CONFLICT
By Rushi Shroff
Now lets try to really understand Ohm's law, which says that the current in a wire is proportional to the voltage. This law isn't really a law at all, not like the force law of gravity or the law of conservation of energy or momentum. In fact it is really rather astonishing that it should be true at all. Why? The voltage produces an electric field in the wire, which produces a force on the electrons. Now this force produces an acceleration (remember Newton: F=MA) not a velocity, thus we would expect the current to grow larger and larger, as the electrons continue to accelerate, moving ever faster. Instead Ohm's law is saying that this constant electric field is producing a constant current, hence constant velocity. Something funny is going on here. To understand this we need to take a closer look at the goings on in the wire. Remember I said that the electrons are like a gas, filling the wire. Well, these electrons are constantly bumping into things, and bouncing off of them. Think of it as follows: Imagine you are in a Ferrari, and you can go from 0 to 100 in 6 seconds. However, you happen to be on a road where there is a stop sign every three seconds. How fast, on the average do you travel? In three seconds, you've accelerated from 0 to 50. Your average speed during those three seconds was 25MPH. Then you had to slam on the brakes, screech to a halt, and start all over again. Thus even though your Ferrari can do 100 in 6 seconds, your average speed is only 25MPH. Hell, you're not even breaking the speed limit (at least on average.)
In the general case, we need to relate
the distance you cover, say L,
to your acceleration, A,
and the amount of time, T you are moving.
At the end of time T,
your velocity V = A * T.
The distance you've covered is your average velocity over that time,
which is V/2, times the time T,
so L = V/2 * T = 1/2 * A * T * T.
Thus if we solve for T we get that
T = Square Root (2 * L / A).
Finally this means that the current,
with is the average velocity of the electrons is 1/2 * A * T = √(L * A / 2).
Take a breath for a moment and let's see what we've discovered.
The current is proportional to some constant,
namely Square Root (L/2) times Square Root(A).
And A, the acceleration, is proportional to the electric field, which is proportional to the voltage.
Oops. We must have made a mistake somewhere, because that is not Ohm's law. Ohm's law says the current is proportional to the voltage, not the square root of the voltage.
What's wrong? Well in a gas, each molecule is constantly moving, because of the thermal energy of the gas. Furthermore, the velocity due to this thermal energy is very large compared to the drift velocity we calculated above.
In fact it is about 10^9 mm/sec or almost 10 orders of magnitude (10^10) times bigger.
Thus their motion is totally random, and very fast.
Therefore the time between collisions is L / thermal velocity, not L / drift velocity.
The fact that this is 10 orders of magnitude greater than the drift velocity means the drift velocity contributes almost nothing to the time.
Thus the average velocity between collisions is 1/2 A * T where T does not depend on A at all. Thus the current is proportional to A which is proportional to the voltage, and voila, we have Ohm's law.
n fact we can squeeze even more information out of this observation. The amount of current flowing down a section of wire is:
the distance you cover, say L,
to your acceleration, A,
and the amount of time, T you are moving.
At the end of time T,
your velocity V = A * T.
The distance you've covered is your average velocity over that time,
which is V/2, times the time T,
so L = V/2 * T = 1/2 * A * T * T.
Thus if we solve for T we get that
T = Square Root (2 * L / A).
Finally this means that the current,
with is the average velocity of the electrons is 1/2 * A * T = √(L * A / 2).
Take a breath for a moment and let's see what we've discovered.
The current is proportional to some constant,
namely Square Root (L/2) times Square Root(A).
And A, the acceleration, is proportional to the electric field, which is proportional to the voltage.
Oops. We must have made a mistake somewhere, because that is not Ohm's law. Ohm's law says the current is proportional to the voltage, not the square root of the voltage.
What's wrong? Well in a gas, each molecule is constantly moving, because of the thermal energy of the gas. Furthermore, the velocity due to this thermal energy is very large compared to the drift velocity we calculated above.
In fact it is about 10^9 mm/sec or almost 10 orders of magnitude (10^10) times bigger.
Thus their motion is totally random, and very fast.
Therefore the time between collisions is L / thermal velocity, not L / drift velocity.
The fact that this is 10 orders of magnitude greater than the drift velocity means the drift velocity contributes almost nothing to the time.
Thus the average velocity between collisions is 1/2 A * T where T does not depend on A at all. Thus the current is proportional to A which is proportional to the voltage, and voila, we have Ohm's law.
n fact we can squeeze even more information out of this observation. The amount of current flowing down a section of wire is:
current density (I) =
The number of atoms per unit volume (N)
times
the number of free electrons per atom (f)
times
the charge per electron (q)
the number of free electrons per atom (f)
times
the charge per electron (q)
times
the average velocity of the electron (1/2 A * T)
the average velocity of the electron (1/2 A * T)
thus: I = 1/2 * N * f * q * A * T
now acceleration A = Force / mass of electron (m) = E / m
and time T = distance between collision L / thermal Velocity V
so I = (N * f * L * q^2 / 2 m V) * E
What have we here? Well, we can see that the stuff in the parentheses, which are all things that depend on the material the wire is made of, is a first order formula for the conductivity. Conductivity is the inverse of resistance, so if we stick all that stuff on the other side of the equation we get:
E (voltage) = (2 m V / N * f * L * q^2) I .... Ohm's law
Which correctly predicts that the resistance should increase as the thermal velocity of the electrons gets larger, or in other words, resistance goes up with temperature, a well know fact.
Now the resistance of a metal like copper is essentially zero, but the resistance of the bulb is substantial. Thus there are a lot more collisions taking place in the filament than in the wire, and guess what, the filament gets hot. The electrical force is being converted into heat, and eventually light by the resistance of the filament, in other words, the flashlight produces light.
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