diff --git a/content/.trash/Homework_1.md b/content/.trash/Homework_1.md new file mode 100644 index 000000000..fc43600d0 --- /dev/null +++ b/content/.trash/Homework_1.md @@ -0,0 +1,8 @@ +--- +title: Homework 1, student's Problem +tags: + - work-about +--- + +# 0780 + diff --git a/content/.trash/Problem.md b/content/.trash/Problem.md new file mode 100644 index 000000000..3c6fbc30e --- /dev/null +++ b/content/.trash/Problem.md @@ -0,0 +1,8 @@ +--- +title: Problem +tags: + - research-about +--- +* UWB signal ejection +* S parameter -> Frequency spectrum +* Know why VNA don't have time domain (circuit view) \ No newline at end of file diff --git a/content/.gitkeep b/content/.trash/UWB.md similarity index 100% rename from content/.gitkeep rename to content/.trash/UWB.md diff --git a/content/.trash/Untitled 10.md b/content/.trash/Untitled 10.md new file mode 100644 index 000000000..e69de29bb diff --git a/content/.trash/Untitled 11.md b/content/.trash/Untitled 11.md new file mode 100644 index 000000000..e69de29bb diff --git a/content/.trash/Untitled 12.md b/content/.trash/Untitled 12.md new file mode 100644 index 000000000..e69de29bb diff --git a/content/.trash/Untitled 2.md b/content/.trash/Untitled 2.md new file mode 100644 index 000000000..e69de29bb diff --git a/content/.trash/Untitled 3.md b/content/.trash/Untitled 3.md new file mode 100644 index 000000000..e69de29bb diff --git a/content/.trash/Untitled 4.md b/content/.trash/Untitled 4.md new file mode 100644 index 000000000..e69de29bb diff --git a/content/.trash/Untitled 5.md b/content/.trash/Untitled 5.md new file mode 100644 index 000000000..e69de29bb diff --git a/content/.trash/Untitled 6.md b/content/.trash/Untitled 6.md new file mode 100644 index 000000000..e69de29bb diff --git a/content/.trash/Untitled 7.md b/content/.trash/Untitled 7.md new file mode 100644 index 000000000..e69de29bb diff --git a/content/.trash/Untitled 8.md b/content/.trash/Untitled 8.md new file mode 100644 index 000000000..e69de29bb diff --git a/content/.trash/Untitled 9.md b/content/.trash/Untitled 9.md new file mode 100644 index 000000000..e69de29bb diff --git a/content/.trash/Untitled.canvas b/content/.trash/Untitled.canvas new file mode 100644 index 000000000..9e26dfeeb --- /dev/null +++ b/content/.trash/Untitled.canvas @@ -0,0 +1 @@ +{} \ No newline at end of file diff --git a/content/.trash/Untitled.md b/content/.trash/Untitled.md new file mode 100644 index 000000000..e69de29bb diff --git a/content/.trash/VNA/IFBW.md b/content/.trash/VNA/IFBW.md new file mode 100644 index 000000000..036c05290 --- /dev/null +++ b/content/.trash/VNA/IFBW.md @@ -0,0 +1,8 @@ +--- +title: Intermediate Frequency Bandwidth +tags: + - equipment + - VNA + - research-about +--- + diff --git a/content/.trash/attachments/Pasted image 20230918104114.png b/content/.trash/attachments/Pasted image 20230918104114.png new file mode 100644 index 000000000..51ed6092c Binary files /dev/null and b/content/.trash/attachments/Pasted image 20230918104114.png differ diff --git a/content/.trash/attachments/mop.23107.pdf b/content/.trash/attachments/mop.23107.pdf new file mode 100644 index 000000000..586a37ef2 Binary files /dev/null and b/content/.trash/attachments/mop.23107.pdf differ diff --git a/content/.trash/equip_res_MOC.md b/content/.trash/equip_res_MOC.md new file mode 100644 index 000000000..8e14d2fb8 --- /dev/null +++ b/content/.trash/equip_res_MOC.md @@ -0,0 +1,6 @@ +--- +title: Equipment Research MOC +tags: + - MOC +--- + diff --git a/content/.trash/experiment_design.md b/content/.trash/experiment_design.md new file mode 100644 index 000000000..5c6aeabf0 --- /dev/null +++ b/content/.trash/experiment_design.md @@ -0,0 +1,78 @@ +--- +title: UWB signal characterization experiment by VNA demo +tags: + - experiment +--- + + +# Experiment Graph Overview + +![](research_career/attachments/Untitled-1.png) + + +In this experiment, we use VNA Port 1 to eject signal and port2 to receive the signal reflecting by the reflection medium, such as burned tissue. + +And we can use VNA to get scattering parameter to do analysis in frequency spectrum, including amplitude information and phase information. + +# Experiment Explanations + +## What is VNA + +![](research_career/attachments/Pasted%20image%2020231016082202.png) + +A Vector Network Analyzer (VNA) is a sophisticated electronic instrument used in the field of radio frequency (RF) and microwave engineering. Its primary function is to measure and characterize the electrical behavior of high-frequency components, such as antennas, cables, and passive RF devices like filters and amplifiers. VNAs are essential tools in the design, testing, and maintenance of RF and microwave systems. +## Ejecting Signal + +The VNA generates an "ejecting signal," also known as the "incident signal" or "test signal", which is usually be a continuous wave (CW) or narrowband signal. In our VNA equipment, the signal is CW signal, which is at discrete frequencies sweeping in the specific frequency range. + +Here I want to name the signal, which is at discrete frequencies sweeping in the specific frequency range, **frequency sweeping signal** + +**So we can not acquire UWB signal directly in VNA.** + +Here are two possible solutions: + +1. Modem our sweep signal to UWB signal. + * I have already find the way to modem chirp signal to UWB signal, here: + [Chirp BOK BPSK.pdf](https://pinktalk.online/research_career/attachments/CN101267424A.pdf) + * Not sure if we can modem our frequency sweeping signal to UWB signal. + +2. Direct using our frequency sweeping signal. + * Though we don't directly eject UWB signal, our ejecting signal also contains discrete frequencies, which are composition of UWB signal. In this way, we can analysis different frequencies component in UWB separately. + * Speculatively, we guess the high frequency part's phase information can provide the range detection function. The low frequency part's amplitude information will have a relation with the reflecting medium. + +In this experiment demo, we use solution 2. + +## Data we get + +In this experiment, we can only get scattering parameter, S11 and S12. + +![](research_career/attachments/Pasted%20image%2020231016091540.png) + +Using this parameter, considering incident as a constant we can get frequency spectrum information, though the signal is not UWB signal + +# Experiment Step + +## 1. Set up Experiment equipment + +* Prepare the experimental apparatus + * VNA, Keysight E5063A 100kHz - 6.5GHz + * UWB antennas + * N, male - SMA male + +* VNA calibration +* Load the UWB antennas to VNA port1 and port2 + + +## 2. Set reference data + +* In antenna's near field and far filed, such as 20cm and 40cm, we need to set a specified medium and get S11 and S12 trace data. +* This two experiments will be our reference. Later we can get other S11 and S12 to compare with this data get range and material. + + +## 3. Data collection + +Collect S11 and S12 trace in different reflection mediums and distances between antennas and mediums. + +## 4. Data analysis + +We want to build relationship between our data with distance and reflection mediums to show that UWB can have the ability to detect burning tissue level. \ No newline at end of file diff --git a/content/.trash/log_06072023.md b/content/.trash/log_06072023.md new file mode 100644 index 000000000..a9ff6c135 --- /dev/null +++ b/content/.trash/log_06072023.md @@ -0,0 +1,8 @@ +--- +title: Log 2023.07.06 - 路过人间，谁有意见 +tags: +- log +- music +--- + +![](文学/log/2023/7/attachments/7JEC(63A65[8JFI[G6O`IIK_tmb.jpg) \ No newline at end of file diff --git a/content/.trash/log_11092023.md b/content/.trash/log_11092023.md new file mode 100644 index 000000000..ed0653cdf --- /dev/null +++ b/content/.trash/log_11092023.md @@ -0,0 +1,7 @@ +--- +title: Log 2023.09.11 - Get some interesting blog here +tags: + - log + - front-end +--- +* [_Building a Frontend Framework; Reactivity and Composability With Zero Dependencies_. https://18alan.space/posts/how-hard-is-it-to-build-a-frontend-framework.html. Accessed 11 Sept. 2023.](https://18alan.space/posts/how-hard-is-it-to-build-a-frontend-framework.html) \ No newline at end of file diff --git a/content/.trash/log_18092023.md b/content/.trash/log_18092023.md new file mode 100644 index 000000000..b00ee053e --- /dev/null +++ b/content/.trash/log_18092023.md @@ -0,0 +1,8 @@ +--- +title: Log 2023.09.18 - A Normal Learning Day +tags: + - log +--- + +* learn 红色高棉 by wiki +* try to use [TXYZ](https://txyz.ai/) to read paper \ No newline at end of file diff --git a/content/.trash/spectrum_analyzer.md b/content/.trash/spectrum_analyzer.md new file mode 100644 index 000000000..63e8dc279 --- /dev/null +++ b/content/.trash/spectrum_analyzer.md @@ -0,0 +1,26 @@ +--- +title: Spectrum Analyzer +tags: + - equipment + - research-about +--- + +# What is spectrum analyzer? + +Measure input signal power spectrum +# Spectrum Analyzer for UWB + +## Papers + +### Measurements of UWB through-the-wall propagation using spectrum analyzer and the Hilbert transform + + +[*pdf* - Measurements of UWB through-the-wall propagation using spectrum analyzer and the Hilbert transform](https://pinktalk.online/equipment_research/attachments/mop.23107.pdf) + +![Architect](signal_processing/equipment/attachments/Pasted%20image%2020230918104114.png) + + +# Reference + +* [_Understanding Basic Spectrum Analyzer Operation_. _www.youtube.com_, https://www.youtube.com/watch?v=P5gxNGckjLc. Accessed 13 Sept. 2023.](https://pinktalk.online/%E6%96%87%E5%AD%A6/%E5%8F%A5%E5%AD%90/Feeling/) +* https://www.bilibili.com/video/BV1kG4y1q72V/?spm_id_from=333.337.search-card.all.click&vd_source=c47136abc78922800b17d6ce79d6e19f \ No newline at end of file diff --git a/content/Math/MOC.md b/content/Math/MOC.md new file mode 100644 index 000000000..b22784085 --- /dev/null +++ b/content/Math/MOC.md @@ -0,0 +1,24 @@ +--- +title: Math MOC +tags: +- math +- MOC +--- + +# Statistics + +## Basic concept + +* [Quantile](Math/Statistics/Basic/Quantile.md) + +# Discrete mathematics + +## Set theory + +* [Cantor Expansion](Math/discrete_mathematics/set_theory/cantor_expansion/cantor_expansion.md) + + +# Optimization Problem + + +* [Quadratic Programming](Math/optimization_problem/Quadratic_Programming.md) \ No newline at end of file diff --git a/content/Math/Statistics/Basic/Quantile.md b/content/Math/Statistics/Basic/Quantile.md new file mode 100644 index 000000000..830d54c14 --- /dev/null +++ b/content/Math/Statistics/Basic/Quantile.md @@ -0,0 +1,17 @@ +--- +title: Quantile +tags: +- math +- statistics +- basic +--- + +**分位数**（英语：Quantile），亦称**分位点**，是指用分割点（cut point）将一个随机变量的概率分布范围分为几个具有相同概率的连续区间。分割点的数量比划分出的区间少1，例如3个分割点能分出4个区间。 + +常见的分位数包括中位数（二分位数）、四分位数（四分位数）和百分位数。 + +1. 中位数：中位数是将一组数据按照大小排序后，处于中间位置的值。将数据分成两部分，有一半的观察值小于中位数，另一半的观察值大于中位数。 + +2. 四分位数：四分位数将数据分成四个等分，分别是下四分位数（25%分位数）、中位数（50%分位数）和上四分位数（75%分位数）。下四分位数是将数据排序后，处于25%位置的值；中位数是处于50%位置的值；上四分位数是处于75%位置的值。 + +3. 百分位数：百分位数将数据分成100个等分，可以表示某个特定百分比处的数据值。例如，75%的百分位数表示将数据排序后，处于75%位置的值 \ No newline at end of file diff --git a/content/Math/discrete_mathematics/set_theory/cantor_expansion/cantor_expansion.md b/content/Math/discrete_mathematics/set_theory/cantor_expansion/cantor_expansion.md new file mode 100644 index 000000000..f6dd54860 --- /dev/null +++ b/content/Math/discrete_mathematics/set_theory/cantor_expansion/cantor_expansion.md @@ -0,0 +1,213 @@ +--- +title: Cantor expansion +tags: +- code-design +- basic +- math +- algorithm +- discrete-mathematics +- set-theory +--- + + +康托展开（Cantor expansion），也称为康托编码（Cantor encoding），是由德国数学家乔治·康托（Georg Cantor）于19世纪末提出的一种数学技术。它用于将**一个无限序列的数字（或有限序列的数字）映射到一个唯一的实数，从而实现序列的编码和排序。** + +# Objective + +康托展开与逆展开是*将全排列和它的字典序互相转化*的两种算法 + +# Application + +* 作为枚举问题的hash function + +# Step by Step + +## Deriving Cantor Expansion + +### Lemma1 and Lemma2 + +以DFS生成的4阶全排列为例~~*(no this algorithm detail here)*~~，带编号： + +```text +0 1 2 3 4 +1 1 2 4 3 +2 1 3 2 4 +3 1 3 4 2 +4 1 4 2 3 +5 1 4 3 2 +6 2 1 3 4 +7 2 1 4 3 +8 2 3 1 4 +9 2 3 4 1 +10 2 4 3 1 +11 2 4 3 1 +12 3 1 2 4 +13 ... +``` + + +可以发现，首位为 1 的全排列表示的数全部在区间 [0,5] ；首位为 2 的全排列全部在区间 [6,11]；首位为 3 的则在 [12,17] ；4 的在 [18,23] 。因为首位有 4 种取值的可能，所以把所有的 4 阶全排列划分成了 4 个长度为 $\frac{4!}{4}=3!=6$ 的区间，首位为 1 的处在第 1 个这样长为 6 的区间，首位为 2 的处在第 2 个，首位为 3 的处在第 3 个…… + +> [!Lemma1] +> 衍生到一般情况，对于首位为$k$的$n$阶全排列，它所在的区间为：$[(k-1) \times (n-1)!,\quad k \times (n-1)!]$ + +在确定大致范围后，如何定位到具体的编号呢？ + +观察遮住第一位的情况： + +```text +0 X 2 3 4 <==> 1 2 3 +1 X 2 4 3 <==> 1 3 2 +2 X 3 2 4 <==> 2 1 3 +3 X 3 4 2 <==> 2 3 1 +4 X 4 2 3 <==> 3 1 2 +5 X 4 3 2 <==> 3 2 1 +6 X 1 3 4 <==> 1 2 3 +7 X 1 4 3 <==> 1 3 2 +8 X 3 1 4 <==> 2 1 3 +9 X 3 4 1 <==> 2 3 1 +10 X 4 3 1 <==> 3 1 2 +11 X 4 3 1 <==> 3 2 1 +12 X 1 2 4 <==> 1 2 3 +13 ... +``` + +观察上表我们发现，**只考虑元素间的相对大小关系**（或者说各个数字——表示相对大小的符号，之间的相对大小关系），*遮掉首位的 4 阶全排列可以认为就是 3 阶全排列*，只不过它们使用的数字（表示大小的符号）不同。 + +> [!Lemma2] +> 所以我们推导$n$阶全排列对应的$(n-1)$阶全排列，如上面所示，去掉首位后，需要对每个能与**首位构成顺序的数字**(*即，比首位数字大的数*)自减少1 + +### Calculate Series index by Lemmas + +对于任意序列，迭代使用引理1和引理2就可以得到它的index。 + +#### Step +1. 利用**引理 1**确定与它同阶同首位的全排列表示的数字的范围，取左边界累加到结果上 +2. 利用**引理 2**将$n$阶全排列转化为$(n-1)$阶全排列 +3. 得到1阶全排列前，重复1，2；得到1阶全排列后输出结果； + +#### Example + +$$ +35142 \rightarrow 3\dot{5}1\dot{4}2 \rightarrow 34132 \rightarrow 341\dot{3}\dot{2} \rightarrow 34121 +$$ + +$$ +index = (3-1) \times 4! + (4-1) \times 3! + (1-1) \times 2! + (2-1) \times 1! = 67 +$$ + +## Definition + +> [!hint] +> 顺序对是由在两个在序列中的元素组成的有序对，它前项在序列中的位置比后项靠前，且前项小于后项。 + +$a_{1\cdots n}$表示一个n阶的全排列，$a_i$表示这个全排列的$i$的数字，定义$a_{1\cdots n}$的退位序列为$b_{1\cdots n}$, $b_j$等于$a_j$在全排列中作顺序对后项的顺序对个数，形式为: +$$ +\forall \ 1 \leq j \leq n, b_j = |\{(a_i, a_j) \ | \ 1 \leq i \leq j \ \text{and} \ a_i \leq a_j\}| +$$ + +其康托展开公式为： +$$ +F(a_{1\cdots n}) = \sum_{i=1}^n (a_i-b_i-1)\times(n-i)! +$$ + + +# Code + +## Method 1 + +直接用定义写出，但是不生成$b$序列，只在用到时求当时的$b_i$ + +```python +class CantorExpansion(): + def cantor_encode(self, s:list) -> int: + + ''' + Encode a list of integers to a single integer using Cantor expansion. + ''' + + count = 0 + + for i in range(len(s)): + count += self.factorial(len(s) - i - 1) * (s[i] - self.count_smaller(s, i) - 1) + + return count + + def factorial(self, x:int) -> int: + if x == 1 or x == 0: + return 1 + else: + return self.factorial(x - 1) * x + + def count_smaller(self, s:list, i:int) -> int: + count = 0 + for j in range(i): + if s[j] < s[i]: + count += 1 + return count +``` + +python file goto: [cantor_expansion.py](https://github.com/PinkR1ver/Jude.W-s-Knowledge-Brain/blob/master/Math/discrete_mathematics/set_theory/cantor_expansion/code/cantor_expansion.py) + +复杂度会是$\varTheta(n^2)$ + +## Method 2 + +再次明确顺序对的概念： + +> [!tip] +> 顺序对是指数组中的一对元素arr[i]和arr[j]，其中i < j且arr[i] > arr[j] + +遍历每一个数的时候，需要计算`count_smaller(s,i)`，因此复杂度被提升到$\varTheta(n^2)$。 + +其实`count_smaller(s,i)`这个方法的目的就是计算数组的顺序对，提高计算数组顺序对的高速算法可以提高算法的复杂度。 + +树状数组（Fenwick Tree）是一种用于高效计算[前缀和（Prefix Sum）](tmp_script/prefix_sum.md)的数据结构，它可以在$O(\log{n})$的时间复杂度内完成前缀和的计算和更新操作。 + +### Trick - 使用树状数组求顺序对的详细步骤 + +Step 1: 离散化 为了方便处理，我们首先对值域数组进行离散化处理，将其转化为一个以0为起始索引的连续整数数组。离散化的目的是将原始的值域映射到一个连续的范围内，以便于在树状数组中使用。 + +Step 2: 初始化树状数组 创建一个长度为n+1的树状数组bit，并将所有元素初始化为0。这个额外的元素bit[0]不会被使用，我们只是为了方便计算。 + +Step 3: 统计顺序对 从右往左遍历离散化后的值域数组arr，对于每个元素arr[i]，我们需要统计在其左侧且比它大的元素的个数。 + +在树状数组中，我们可以通过查询前缀和的方式来计算某个位置的值。因此，对于当前的元素arr[i]，我们查询树状数组中索引为arr[i]的前缀和，得到的结果就是arr[i]左侧比它大的元素的个数。 + +Step 4: 更新树状数组 在统计完当前元素的顺序对后，我们需要更新树状数组，以便下一次查询能够正确计算前缀和。具体操作如下： + +- 在树状数组中，将索引为arr[i]的位置的值加1，表示arr[i]的出现次数加1。 +- 重复上述操作，直到遍历完所有元素。 + +Step 5: 计算总顺序对数 完成整个遍历后，树状数组中的每个位置的值表示该值在原始数组中的出现次数。通过查询树状数组的前缀和，我们可以计算出总的顺序对数。 + +--- + +利用上述使用树状数组求顺序对的算法就可以将Cantor Expansion复杂度降低到$\varTheta(n\log{n})$ + + +# Inverse Cantor Expansion + +逆康托展开的思想是用引理1去定位每一个位置 + +Example: + +`inverse_cantor_expansion(n=5, x=96)`: + +* Step 1. 如果是字典序从1开始，则(x - 1) = 95，说明在这个数已经有95个数 +* Step 2. floor(95 / (n-1)!) = floor(95 / 4!) = 3，说明有3个数比第一位小，所以第一位被定位为4，余数为23 +* Step 3. 剩下数字被23定位，floor(23 / 3!) = 3，余数为5，说明有3个数比第二位小，被定位为4，但是4已经出现过，因此是5 +* Step 4. 剩下的数字用5定位，floor(5 / 2!) = 2，余数为1，说明有2个数比第三位小，被定位为3。 +* Step 5. 同理，剩下第四位被定位为2，最后一位被定位为1 + +# Generalized Cantor Expansion + +TODO ... ... + +Generalized Cantor Expansion可能并不能满足双射条件 + +# Reference + +* ChatGPT +* [“【给初心者的】康托展开.” 知乎专栏, https://zhuanlan.zhihu.com/p/39377593. Accessed 6 July 2023.](https://zhuanlan.zhihu.com/p/39377593) + diff --git a/content/Math/discrete_mathematics/set_theory/cantor_expansion/code/cantor_expansion.py b/content/Math/discrete_mathematics/set_theory/cantor_expansion/code/cantor_expansion.py new file mode 100644 index 000000000..14f04533e --- /dev/null +++ b/content/Math/discrete_mathematics/set_theory/cantor_expansion/code/cantor_expansion.py @@ -0,0 +1,63 @@ +class CantorExpansion(): + def cantor_encode(self, s:list) -> int: + + ''' + Encode a list of integers to a single integer using Cantor expansion. + ''' + + count = 0 + + for i in range(len(s)): + count += self.factorial(len(s) - i - 1) * (s[i] - self.count_smaller(s, i) - 1) + + return count + + def cantor_decode(self, x:int, n:int) -> list: + + ''' + Decode a single integer to a list of integers using Cantor expansion. + ''' + + s = [None] * n + used_dict = {} + + for num in range(1, n + 1): + used_dict[num] = False + + + iter = 0 + for i in range(n - 1, -1, -1): + + smaller = x // self.factorial(i) + x %= self.factorial(i) + + count = 0 + for i in range(1, n + 1): + if not used_dict[i]: + count += 1 + if count == smaller + 1: + s[iter] = i + used_dict[i] = True + iter += 1 + break + + return s + + def factorial(self, x:int) -> int: + if x == 1 or x == 0: + return 1 + else: + return self.factorial(x - 1) * x + + def count_smaller(self, s:list, i:int) -> int: + count = 0 + for j in range(i): + if s[j] < s[i]: + count += 1 + return count + + +if __name__ == '__main__': + s = CantorExpansion() + print(s.cantor_encode([3, 5, 7, 4, 1, 2, 9, 6, 8])) + print(s.cantor_decode(0, 9)) diff --git a/content/Math/optimization_problem/Quadratic_Programming.md b/content/Math/optimization_problem/Quadratic_Programming.md new file mode 100644 index 000000000..54a1fa434 --- /dev/null +++ b/content/Math/optimization_problem/Quadratic_Programming.md @@ -0,0 +1,77 @@ +--- +title: Quadratic Programming +tags: + - math + - optimize + - optimization +--- + +# Why I write this note? + +[猪熊一波. _帮女朋友降维打击领导！_哔哩哔哩_bilibili_. https://www.bilibili.com/video/BV1ZN411T7c9/. Accessed 30 Nov. 2023.](https://www.bilibili.com/video/BV1ZN411T7c9/?spm_id_from=333.999.0.0&vd_source=c47136abc78922800b17d6ce79d6e19f) + +# Tips + +> [!tip] +> "Programming" in this context refers to a formal procedure for solving mathematical problems. This usage dates to the 1940s and is not specifically tied to the more recent notion of "computer programming." To avoid confusion, some practitioners prefer the term "optimization" — e.g., "quadratic optimization." +> +> "Programming" 在中文中的翻译可以为“规划”， “Quadratic Programming”的翻译为“二次规划” + +> [!Summary] +> A Quadratic Program(QP) has a quadratic objective function and linear constrains + +# Problem Formulation + +The quadratic programming problem with $n$ variables and $m$ constraints can be formulated as follows. Given: + +* a real-valued, n-dimensional vector $c$, +* an $n\times n$-dimensional real symmetric matrix $Q$, +* an $m \times n$-dimensional real matrix $A$, and +* an $m-dimensional$ real vector $b$ + +the objective of quadratic programming is to find an $n$-dimensional vector $x$, that will + +$$ +\text{minimize} \quad \mathup{\frac{1}{2} x^{T}Qx + c^{T}x}\quad +$$ +$$ +\text{subject to} \quad A\mathup{x} \preceq b +$$ +$$ +\mathup{x} = \begin{bmatrix} +x_1 \\ +x_2 \\ +\vdots \\ +x_n +\end{bmatrix}, \mathup{Q} = +\begin{bmatrix} +Q_{11} & Q_{12} & \cdots & Q_{1n} \\ +\vdots & \vdots & \ddots & \vdots \\ +Q_{n1} & Q_{n2} & \cdots & Q_{nn} +\end{bmatrix}, +\mathup{c} = \begin{bmatrix} +c_1 \\ +c_2 \\ +\vdots \\ +c_n +\end{bmatrix}, +\mathup{A} = +\begin{bmatrix} +A_{11} & A_{12} & \cdots & A_{1m} \\ +\vdots & \vdots & \ddots & \vdots \\ +A_{n1} & A_{n2} & \cdots & A_{nm} +\end{bmatrix}, +\mathup{b} = \begin{bmatrix} +b_1 \\ +b_2 \\ +\vdots \\ +b_n +\end{bmatrix} +$$ + + +# Reference + + +* [猪熊一波. _帮女朋友降维打击领导！_哔哩哔哩_bilibili_. https://www.bilibili.com/video/BV1ZN411T7c9/. Accessed 30 Nov. 2023.](https://www.bilibili.com/video/BV1ZN411T7c9/?spm_id_from=333.999.0.0&vd_source=c47136abc78922800b17d6ce79d6e19f) +* [“Quadratic Programming.” _Wikipedia_, 25 Nov. 2023. _Wikipedia_, https://en.wikipedia.org/w/index.php?title=Quadratic_programming&oldid=1186784717.](https://en.wikipedia.org/wiki/Quadratic_programming#:~:text=Quadratic%20programming%20(QP)%20is%20the,linear%20constraints%20on%20the%20variables.) diff --git a/content/Math/real_analysis/attachments/6BC0B163CEFCF127E1D70326AB7D1648 1.png b/content/Math/real_analysis/attachments/6BC0B163CEFCF127E1D70326AB7D1648 1.png new file mode 100644 index 000000000..694805276 Binary files /dev/null and b/content/Math/real_analysis/attachments/6BC0B163CEFCF127E1D70326AB7D1648 1.png differ diff --git a/content/Math/real_analysis/attachments/6BC0B163CEFCF127E1D70326AB7D1648.png b/content/Math/real_analysis/attachments/6BC0B163CEFCF127E1D70326AB7D1648.png new file mode 100644 index 000000000..694805276 Binary files /dev/null and b/content/Math/real_analysis/attachments/6BC0B163CEFCF127E1D70326AB7D1648.png differ diff --git a/content/Math/real_analysis/attachments/78DC2683DB0DF2EFEB6215DAB8C18C25.png b/content/Math/real_analysis/attachments/78DC2683DB0DF2EFEB6215DAB8C18C25.png new file mode 100644 index 000000000..02bff2bb9 Binary files /dev/null and b/content/Math/real_analysis/attachments/78DC2683DB0DF2EFEB6215DAB8C18C25.png differ diff --git a/content/Math/real_analysis/cauchy_principal_value.md b/content/Math/real_analysis/cauchy_principal_value.md new file mode 100644 index 000000000..9c8e35e2c --- /dev/null +++ b/content/Math/real_analysis/cauchy_principal_value.md @@ -0,0 +1,26 @@ +--- +title: Cauchy Principal Value +tags: + - math + - real-analysis +--- +# Notation + + +$$ +\text{p.v.} \int_{-\infty}^{\infty} f(x)dx = \lim_{a\rightarrow+\infty} \int_{-a}^{a} f(x) dx = \lim_{a\rightarrow+\infty}[f(a) - f(-a)] +$$ + + + +![](Math/real_analysis/attachments/6BC0B163CEFCF127E1D70326AB7D1648%201.png) + + +![](Math/real_analysis/attachments/78DC2683DB0DF2EFEB6215DAB8C18C25.png) + +the Cauchy principal value is the method for assigning values to *certain improper integrals* which would otherwise be undefined. In this method, a singularity on an integral interval is avoided by limiting the integral interval to the non singular domain. + +# Reference + +* [_Real Analysis 64 | Cauchy Principal Value_. _www.youtube.com_, https://www.youtube.com/watch?v=0SP2b0nFpwI. Accessed 3 Jan. 2024.](https://www.youtube.com/watch?v=0SP2b0nFpwI) +* [“Cauchy Principal Value.” _Wikipedia_, 31 Dec. 2023. _Wikipedia_, https://en.wikipedia.org/w/index.php?title=Cauchy_principal_value&oldid=1192842366.](https://en.wikipedia.org/wiki/Cauchy_principal_value) \ No newline at end of file diff --git a/content/Photography/Aesthetic/Landscape/Landscape_MOC.md b/content/Photography/Aesthetic/Landscape/Landscape_MOC.md new file mode 100644 index 000000000..26552df7c --- /dev/null +++ b/content/Photography/Aesthetic/Landscape/Landscape_MOC.md @@ -0,0 +1,9 @@ +--- +title: Landscape Photography MOC +tags: +- photography +- landscape +- MOC +--- + +* [🌊Sea MOC](Photography/Aesthetic/Landscape/Sea/Sea_MOC.md) \ No newline at end of file diff --git a/content/Photography/Aesthetic/Landscape/Sea/Fujifilm_Blue_by_小红书_Philips谢骏.md b/content/Photography/Aesthetic/Landscape/Sea/Fujifilm_Blue_by_小红书_Philips谢骏.md new file mode 100644 index 000000000..6e6f0fccc --- /dev/null +++ b/content/Photography/Aesthetic/Landscape/Sea/Fujifilm_Blue_by_小红书_Philips谢骏.md @@ -0,0 +1,29 @@ +--- +title: Sea in Fujiflm Blue +tags: +- photography +- landscape +- photography +--- + +![](Photography/Aesthetic/Landscape/Sea/attachments/Pasted%20image%2020230420014349.png) + + +![](Photography/Aesthetic/Landscape/Sea/attachments/Pasted%20image%2020230420014354.png) + + +![](Photography/Aesthetic/Landscape/Sea/attachments/Pasted%20image%2020230420014401.png) + + +![](Photography/Aesthetic/Landscape/Sea/attachments/Pasted%20image%2020230420014613.png) + + +![](Photography/Aesthetic/Landscape/Sea/attachments/Pasted%20image%2020230420014622.png) + + +![](Photography/Aesthetic/Landscape/Sea/attachments/Pasted%20image%2020230420014634.png) + +# Reference + +* [太绝了！我拍出了富士蓝！- 小红书，Philips谢骏](https://www.xiaohongshu.com/user/profile/6272c025000000002102353b/641299a200000000130129bb) + diff --git a/content/Photography/Aesthetic/Landscape/Sea/Sea_MOC.md b/content/Photography/Aesthetic/Landscape/Sea/Sea_MOC.md new file mode 100644 index 000000000..5678f48d8 --- /dev/null +++ b/content/Photography/Aesthetic/Landscape/Sea/Sea_MOC.md @@ -0,0 +1,11 @@ +--- +title: 🌊Sea MOC +tags: + - landscape + - sea + - photography + - aesthetic +--- + +* [Fujifilm Blue🌊, 小红书-Philips谢骏](Photography/Aesthetic/Landscape/Sea/Fujifilm_Blue_by_小红书_Philips谢骏.md) +* [豊島🏝, Instagram-shiifoncake](Photography/Aesthetic/Landscape/Sea/豊島_Instagram_shiifoncake.md) \ No newline at end of file diff --git a/content/Photography/Aesthetic/Landscape/Sea/attachments/Pasted image 20230420014349.png b/content/Photography/Aesthetic/Landscape/Sea/attachments/Pasted image 20230420014349.png new file mode 100644 index 000000000..08673ce6e Binary files /dev/null and b/content/Photography/Aesthetic/Landscape/Sea/attachments/Pasted image 20230420014349.png differ diff --git a/content/Photography/Aesthetic/Landscape/Sea/attachments/Pasted image 20230420014354.png 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b/content/Photography/Aesthetic/Landscape/Sea/attachments/shiifoncake_339164445_155642070453847_6842139942547564019_n.jpg differ diff --git a/content/Photography/Aesthetic/Landscape/Sea/豊島_Instagram_shiifoncake.md b/content/Photography/Aesthetic/Landscape/Sea/豊島_Instagram_shiifoncake.md new file mode 100644 index 000000000..968724aeb --- /dev/null +++ b/content/Photography/Aesthetic/Landscape/Sea/豊島_Instagram_shiifoncake.md @@ -0,0 +1,24 @@ +--- +title: 豊島🏝 +tags: + - photography + - sea + - landscape + - aesthetic +--- +![](Photography/Aesthetic/Landscape/Sea/attachments/shiifoncake_338949220_771246770941652_287141902256013940_n.jpg) + +![](Photography/Aesthetic/Landscape/Sea/attachments/shiifoncake_339164445_155642070453847_6842139942547564019_n%20(1).jpg) + +![](Photography/Aesthetic/Landscape/Sea/attachments/shiifoncake_339164445_155642070453847_6842139942547564019_n.jpg) + +![](Photography/Aesthetic/Landscape/Sea/attachments/shiifoncake_338803198_1141886276488589_5464974698780309052_n%20(1).jpg) + +![](Photography/Aesthetic/Landscape/Sea/attachments/shiifoncake_338803198_1141886276488589_5464974698780309052_n.jpg) + +![](Photography/Aesthetic/Landscape/Sea/attachments/shiifoncake_338758486_601356648715316_3737336679741136784_n.jpg) + + +# Reference + +* (https://www.instagram.com/p/Cqh4Ci8vV5u/)[https://www.instagram.com/p/Cqh4Ci8vV5u/] \ No newline at end of file diff --git a/content/Photography/Aesthetic/Polaroid/Polaroid_aesthetic_MOC.md b/content/Photography/Aesthetic/Polaroid/Polaroid_aesthetic_MOC.md new file mode 100644 index 000000000..dd50f5e4d --- /dev/null +++ b/content/Photography/Aesthetic/Polaroid/Polaroid_aesthetic_MOC.md @@ -0,0 +1,9 @@ +--- +title: Polaroid Aestheic MOC +tags: +- photography +- Polaroid +- MOC +--- + +* [🖼How to show Polaroid photo in a great way](Photography/Aesthetic/Polaroid/Polaroid_showcase.md) \ No newline at end of file diff --git a/content/Photography/Aesthetic/Polaroid/Polaroid_showcase.md b/content/Photography/Aesthetic/Polaroid/Polaroid_showcase.md new file mode 100644 index 000000000..c19b8336c --- /dev/null +++ b/content/Photography/Aesthetic/Polaroid/Polaroid_showcase.md @@ -0,0 +1,25 @@ +--- +title: How to show Polaroid photo in a great way +tags: +- photography +- Polaroid +- share +--- + + + +![](Photography/Aesthetic/Polaroid/attachments/IMG_5330.jpg) + + + +![](Photography/Aesthetic/Polaroid/attachments/IMG_5329.jpg) + + + +![](Photography/Aesthetic/Polaroid/attachments/IMG_5327.jpg) + + + +![](Photography/Aesthetic/Polaroid/attachments/IMG_5334.jpg) + +Credits to [比扫描仪更easy的宝丽来翻拍解决方案 -BonBon的Pan](https://www.xiaohongshu.com/user/profile/6272c025000000002102353b/6331af53000000001701acfd) \ No newline at end of file diff --git a/content/Photography/Aesthetic/Polaroid/attachments/IMG_5327.jpg b/content/Photography/Aesthetic/Polaroid/attachments/IMG_5327.jpg new file mode 100644 index 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--git a/content/Photography/Aesthetic/Portrait/Flower_and_Girl.md b/content/Photography/Aesthetic/Portrait/Flower_and_Girl.md new file mode 100644 index 000000000..a3c29bbac --- /dev/null +++ b/content/Photography/Aesthetic/Portrait/Flower_and_Girl.md @@ -0,0 +1,53 @@ +--- +title: 🌸Flower & Girl +tags: +- photography +- portrait +- 摘抄 +--- + +Credits to [Marta Bevacqua](https://www.martabevacquaphotography.com/), +Thanks🌸 + +![](Photography/Aesthetic/Portrait/attachments/14.jpg) + +![](Photography/Aesthetic/Portrait/attachments/15.jpg) + +![](Photography/Aesthetic/Portrait/attachments/16.jpg) + +![](Photography/Aesthetic/Portrait/attachments/17.jpg) + +![](Photography/Aesthetic/Portrait/attachments/18.jpg) + +![](Photography/Aesthetic/Portrait/attachments/19.jpg) + +![](Photography/Aesthetic/Portrait/attachments/20.jpg) + +![](Photography/Aesthetic/Portrait/attachments/21.jpg) + +![](Photography/Aesthetic/Portrait/attachments/22.jpg) + +![](Photography/Aesthetic/Portrait/attachments/content%20(1).jpg) + +![](Photography/Aesthetic/Portrait/attachments/content%20(2).jpg) + +![](Photography/Aesthetic/Portrait/attachments/content%20(3).jpg) + +![](Photography/Aesthetic/Portrait/attachments/content%20(4).jpg) + +![](Photography/Aesthetic/Portrait/attachments/content%20(5).jpg) + +![](Photography/Aesthetic/Portrait/attachments/content%20(6).jpg) + +![](Photography/Aesthetic/Portrait/attachments/content%20(7).jpg) + +![](Photography/Aesthetic/Portrait/attachments/content%20(8).jpg) + +![](Photography/Aesthetic/Portrait/attachments/content%20(9).jpg) + +![](Photography/Aesthetic/Portrait/attachments/content%20(11).jpg) + +![](Photography/Aesthetic/Portrait/attachments/content%20(12).jpg) + +![](Photography/Aesthetic/Portrait/attachments/content.jpg) + diff --git a/content/Photography/Aesthetic/Portrait/From Korean MV Todays_Mod.md b/content/Photography/Aesthetic/Portrait/From Korean MV Todays_Mod.md new file mode 100644 index 000000000..45ea7fb1a --- /dev/null +++ b/content/Photography/Aesthetic/Portrait/From Korean MV Todays_Mod.md @@ -0,0 +1,35 @@ +--- +title: Cute Portrait from Korean MV +tags: +- photography +- portrait +- korean +- cute +- 摘抄 +--- + +Credits to [MV - CHEEZE(치즈) _ Today's Mood(오늘의 기분)](https://www.youtube.com/watch?v=zRq_DlEzygk), +Thanks + +Also, I see this in [摄影灵感｜那有一点可爱 - by +小八怪](https://www.xiaohongshu.com/explore/63f0a27e0000000013002b05) + +![](Photography/Aesthetic/Portrait/attachments/photo_4_2023-03-27_23-53-20.jpg) + +![](Photography/Aesthetic/Portrait/attachments/photo_5_2023-03-27_23-53-20.jpg) + +![](Photography/Aesthetic/Portrait/attachments/photo_6_2023-03-27_23-53-20.jpg) + +![](Photography/Aesthetic/Portrait/attachments/photo_7_2023-03-27_23-53-20.jpg) + +![](Photography/Aesthetic/Portrait/attachments/photo_8_2023-03-27_23-53-20.jpg) + +![](Photography/Aesthetic/Portrait/attachments/photo_9_2023-03-27_23-53-20.jpg) + +![](Photography/Aesthetic/Portrait/attachments/photo_1_2023-03-27_23-53-20%201.jpg) + +![](Photography/Aesthetic/Portrait/attachments/photo_2_2023-03-27_23-53-20%201.jpg) + +![](Photography/Aesthetic/Portrait/attachments/photo_3_2023-03-27_23-53-20%201.jpg) + +![](Photography/Aesthetic/Portrait/attachments/photo_2023-03-27_23-55-45.jpg) \ No newline at end of file diff --git a/content/Photography/Aesthetic/Portrait/Portrait_MOC.md b/content/Photography/Aesthetic/Portrait/Portrait_MOC.md new file mode 100644 index 000000000..03fc68e91 --- /dev/null +++ b/content/Photography/Aesthetic/Portrait/Portrait_MOC.md @@ -0,0 +1,11 @@ +--- +title: 👧Portrait +tags: +- photography +- portrait +- 摘抄 +- MOC +--- + +* [🌸Flower & Girl](Photography/Aesthetic/Portrait/Flower_and_Girl.md) +* [👧🇰🇷Cute Portrait from Korean MV ](Photography/Aesthetic/Portrait/From%20Korean%20MV%20Todays_Mod.md) diff --git a/content/Photography/Aesthetic/Portrait/attachments/14.jpg 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+- style +- share +--- + +![](Photography/Aesthetic/Style/attachments/cinematicshine_326914596_601425291912114_4038822895364546166_n.jpg) + + +![](Photography/Aesthetic/Style/attachments/cinematicshine_341207739_637183131584785_7839745357939483631_n.jpg) + + +# Reference + +* [https://www.instagram.com/p/CrGoBoeo8NF/](https://www.instagram.com/p/CrGoBoeo8NF/) \ No newline at end of file diff --git a/content/Photography/Aesthetic/Style/Style_MOC.md b/content/Photography/Aesthetic/Style/Style_MOC.md new file mode 100644 index 000000000..33506ad28 --- /dev/null +++ b/content/Photography/Aesthetic/Style/Style_MOC.md @@ -0,0 +1,11 @@ +--- +title: ☝Style +tags: +- photography +- style +- share +- MOC +--- + +* [🌅Warmth - Nguan](Photography/Aesthetic/Style/Warmth_by_Nguan.md) +* [📗 Grainy Green](Photography/Aesthetic/Style/Grainy_Green.md) diff --git a/content/Photography/Aesthetic/Style/Warmth_by_Nguan.md b/content/Photography/Aesthetic/Style/Warmth_by_Nguan.md new file mode 100644 index 000000000..ff4724f45 --- /dev/null +++ b/content/Photography/Aesthetic/Style/Warmth_by_Nguan.md @@ -0,0 +1,26 @@ +--- +title: 🎈Warmth - Nguan +tags: +- share +- photography +--- + +Credits to [Nguan](https://www.instagram.com/_nguan_/) + + +![](Photography/Aesthetic/Style/attachments/167396766_118928406833773_7462235788758622009_n.jpg) + +![](Photography/Aesthetic/Style/attachments/275801921_507726407459443_2779968335661218284_n.jpg) + +![](Photography/Aesthetic/Style/attachments/275101252_116346090976633_4116581661408205933_n.jpg) + + +![](Photography/Aesthetic/Style/attachments/152391470_356387755409221_8144178651765781801_n.jpg) + + +![](Photography/Aesthetic/Style/attachments/153386473_426909131936316_8535520818773302544_n.jpg) + + +![](Photography/Aesthetic/Style/attachments/156216827_337435770999537_8250898900544979316_n.jpg) + + diff --git a/content/Photography/Aesthetic/Style/attachments/152391470_356387755409221_8144178651765781801_n.jpg 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b/content/Photography/Aesthetic/Style/attachments/cinematicshine_341207739_637183131584785_7839745357939483631_n.jpg new file mode 100644 index 000000000..04e0f45fa Binary files /dev/null and b/content/Photography/Aesthetic/Style/attachments/cinematicshine_341207739_637183131584785_7839745357939483631_n.jpg differ diff --git a/content/Photography/Basic/MTF_Curve.md b/content/Photography/Basic/MTF_Curve.md new file mode 100644 index 000000000..4292a8501 --- /dev/null +++ b/content/Photography/Basic/MTF_Curve.md @@ -0,0 +1,95 @@ +--- +title: Modulation transfer function(MTF) Curve +tags: +- photography +- basic +- lens +--- + +有很多因素影响lens performance： + +* diffraction +* optical aberrations +* design criteria and philosophy +* manufacturing tolerances and errors + +一般，可以用MTF Curve来作为一个标准来衡量lens performance + +> [!abstract] +> 本篇笔记会从摄影角度浅浅了解MTF曲线，而不从物理光学角度分析 + +# What is MTF Curve + + +调制传递函数 (MTF) 曲线是一种信息密集型指标(information-dense metric)，反映了镜头如何*将对比度再现为空间频率（分辨率）的函数*。MTF Curve在一组设定好的基础参数下，提供一个composite view，关于光学像差([**optical aberrations**](Physics/Optical/optical_abberation.md))如何影响镜头性能。 + +通过MTF图，我们可以知道 + +1. 分辨率, (*代表着镜头对细节的表现能力*) +2. 对比度, (*代表着镜头表现光线亮和暗的能力*) +3. 色散和横向色差 +4. 像场弯曲 + +不可以知道： + +1. 镜头畸变 +2. 径向色差 +3. 晕影 +4. 眩光 + +# How to measure MTF Curve + +大家应该知道，一个镜头的中心比边缘成像能力要好很多，因此只测试镜头的中心或边缘，是不能代表镜头的好坏的，所以厂家会从中心到边缘，选取多个点进行测试。如下图，尼康的全画幅机器，选取了距离中心5毫米，10mm，15mm，20mm的点测试。如果是APS-C画幅，因为感光元件小，会选取3mm，6mm，9mm，12mm等，不同厂家可能不一样。 + +![](Photography/Basic/attachments/Pasted%20image%2020230424143258.png) + +测试方法一般使用白色背景、黑色直线 + +![](Photography/Basic/attachments/Pasted%20image%2020230424143425.png) + +* **粗线**用来测试**对比度**，粗度为 10 lines/mm +* **细线**用来测试**分辨率**，粗度为 30 lines/mm +* 粗细各有两组，一组与半径平行，叫做Sagittal，另一组与半径垂直，叫做Meridonial，这样做主要是为了测试**色散**和**色差**的。 + +下图的成像质量是越来越差： + +![](Photography/Basic/attachments/Pasted%20image%2020230424143543.png) + +# How to read MTF curve + +![](Photography/Basic/attachments/Pasted%20image%2020230424143711.png) + +横坐标代表了到镜头中心的距离，纵坐标代表了对比度和分辨率的值。 + +最完美的镜头的曲线应该是下面这样的，一条红线一条蓝线， + +红线是通过**粗线**测试得到的，代表**对比度**； + +蓝线是通过**细线**测试得到的，代表**分辨率**。 + +![](Photography/Basic/attachments/Pasted%20image%2020230424143940.png) + +普通的镜头的曲线应该是下面这样的(红线代表对比度，蓝线代表分辨率)，在中心点，镜头的对比度和分辨率最好，越往边缘越差。 + +一般来讲，值大于0.9就代表镜头非常优秀，0.7-0.9是优秀，0.5-0.7就是普通，低于0.5就算差了。 + +注意到线的中级部位有呈波浪状，这表明了镜头的另一个参数素质：像场弯曲(curvature of field)\ + +有波浪就代表有像场弯曲，越大就越严重，实际情况一般问题不大。 + +![](Photography/Basic/attachments/Pasted%20image%2020230424144046.png) + +最常见的MTF曲线如图： + +![](Photography/Basic/attachments/Pasted%20image%2020230424144112.png) + +1. 红线，10lines/mm，也就是上面测试时说的粗线，用来测对比度的，从镜头中心到边缘，数值逐渐降低，表明镜头的对比度从镜头到边缘，逐渐降低。 +2. 分辨率，从中心到边缘逐渐降低 +3. 色散和色差 + * 测试时粗细都有两组线吗，一组与半径平行，另一组垂直，用来测试色散和色差，这样就分别得到两条线，与半径平行的一组得到实线，与半径垂直的一组得到虚线。**虚线实线越接近，代表镜头的色散和色差控制的很好，越背离，表示越严重**。 +4. 像场弯曲 + +# Reference + +* [The Modulation Transfer Function (MTF), https://www.edmundoptics.com](https://www.edmundoptics.com/knowledge-center/application-notes/imaging/modulation-transfer-function-mtf-and-mtf-curves/) +* [MTF 曲线图应该怎么看？, 知乎](https://www.zhihu.com/question/19713211) \ No newline at end of file diff --git a/content/Photography/Basic/Saturation.md b/content/Photography/Basic/Saturation.md new file mode 100644 index 000000000..3b3687485 --- /dev/null +++ b/content/Photography/Basic/Saturation.md @@ -0,0 +1,8 @@ +--- +title: Saturation - 饱和度 +tags: +- basic +- photography +--- + +to be written... \ No newline at end of file diff --git a/content/Photography/Basic/attachments/DGE{QUQ2G`9TD8NE18J3J@T.png b/content/Photography/Basic/attachments/DGE{QUQ2G`9TD8NE18J3J@T.png new file mode 100644 index 000000000..7511669b2 Binary files /dev/null and b/content/Photography/Basic/attachments/DGE{QUQ2G`9TD8NE18J3J@T.png differ diff --git a/content/Photography/Basic/attachments/Pasted image 20230424140836.png 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file mode 100644 index 000000000..9d0b37fe3 --- /dev/null +++ b/content/Photography/Cameras_Research/Pocket_film/Pocket_film_camera_MOC.md @@ -0,0 +1,12 @@ +--- +title: Pocket Film camera MOC +tags: +- photography +- review +- MOC +- camera +--- + +# Rollei + +* [Rollei35](Photography/Cameras_Research/Pocket_film/Rollei_35.md) \ No newline at end of file diff --git a/content/Photography/Cameras_Research/Pocket_film/Rollei_35.md b/content/Photography/Cameras_Research/Pocket_film/Rollei_35.md new file mode 100644 index 000000000..38905ce86 --- /dev/null +++ b/content/Photography/Cameras_Research/Pocket_film/Rollei_35.md @@ -0,0 +1,11 @@ +--- +title: Rollei 35 review +tags: +- photography +- rollei35 +- rollei +- camera +- review +--- + + diff --git a/content/Photography/Cameras_Research/Polaroid/Polaroid.md b/content/Photography/Cameras_Research/Polaroid/Polaroid.md new file mode 100644 index 000000000..b7dd64acc --- /dev/null +++ b/content/Photography/Cameras_Research/Polaroid/Polaroid.md @@ -0,0 +1,25 @@ +--- +title: Polaroid +tags: +- camera +- photography +- MOC +- polaroid +--- + +# Polaroid Background + +![](Photography/Cameras_Research/Polaroid/attachments/Pasted%20image%2020230330195031.png) + +Polaroid是一家成立于1937年的美国相机及照片制造公司，该公司曾经是即时相机市场的领导者。Polaroid公司在20世纪50年代推出了第一台即时相机，并在随后的几十年里不断推出各种型号的即时相机和胶片，成为了全球广泛使用的品牌。 + +Polaroid最著名的特点之一是它的“即时影像”技术，这种技术可以使用户在拍摄后几秒钟内看到他们所拍摄的照片。Polaroid的即时相机成为了许多人记录重要时刻和创造独特艺术作品的选择。 + +除了即时相机，Polaroid还生产和销售其他相机、相机附件、数码相框和照片打印机等产品。此外，Polaroid还与其他品牌合作，推出了许多联名款式的相机和其他产品。 + +在Polaroid成立近90年的历史中，它的相机和胶片已经成为了文化和艺术的象征，并继续影响着人们对摄影和影像创作的认知。 + +# Polaroid Camera Review + +* [Polaroid one600](Photography/Cameras_Research/Polaroid/Polaroid_one600.md) +* [Polaroid Integral 600 Series](Photography/Cameras_Research/Polaroid/Polaroid_600.md) diff --git a/content/Photography/Cameras_Research/Polaroid/Polaroid_600.md b/content/Photography/Cameras_Research/Polaroid/Polaroid_600.md new file mode 100644 index 000000000..f0904a283 --- /dev/null +++ b/content/Photography/Cameras_Research/Polaroid/Polaroid_600.md @@ -0,0 +1,13 @@ +--- +title: Polaroid 600 +tags: +- polaroid +- camera +- review +- photography +--- + +# Reference + +* [How do I use my Vintage Polaroid 600 camera? – Retrospekt](https://retrospekt.com/blogs/ask-the-expert/how-do-i-use-my-vintage-polaroid-600-instant-camera) +* [Polaroid Integral 600 Series - Camera-wiki.org - The free camera encyclopedia](http://camera-wiki.org/wiki/Polaroid_Integral_600_Series) diff --git a/content/Photography/Cameras_Research/Polaroid/Polaroid_one600.md b/content/Photography/Cameras_Research/Polaroid/Polaroid_one600.md new file mode 100644 index 000000000..d5da60176 --- /dev/null +++ b/content/Photography/Cameras_Research/Polaroid/Polaroid_one600.md @@ -0,0 +1,46 @@ +--- +title: # Polaroid One 600 Camera Review +tags: +- camera +- photography +- review +- polaroid +--- + + +![](Photography/Cameras_Research/Polaroid/attachments/Pasted%20image%2020230330195707.png) + +# Specifications + +- **(Wide) 100mm lens with minimum focus distance of 3 feet.** +- **Maximum Aperture F12.9 (Don't know if it can change)** +- **1/200 s to 1/3 s** +- **Fixed focus.** +- Exposure modes - **Program automatic** +- "Aerodynamic" styling (particularly when folded) with downward curve at back. +- Flash moved to right hand side of user and can be manually switched on and off. +- Hand grip on right. +- LCD frame counter. +- Self-timer. + +## Functionally similar models + +- Polaroid One (silver/grey) +- Polaroid One600 Job Pro (black/silver/yellow) (Close-focus to 18 inches!) +- Polaroid One600 Nero (all black) +- Polaroid One600 "Flowers" (white with purple and yellow flower design) +- Polaroid One600 Panna (white/black) +- Polaroid One600 "Poison Frog" (silver/grey with yellow/black pattern) +- Polaroid One600 Polala 2006 (red/silver with gold Chinese dragon) +- Polaroid One600 Pro (all silver) (Like Job Pro, close-focus to 18 inches!) +- Polaroid One600 Royksopp (grey/silver with 'Royksopp - Only This Moment' branding) +- Polaroid One600 Superheadz Special Edition Red Hat (silver/black, with 'red hat' cartoon character) +- Polaroid One600 Rossa (bright red/black) +- Polaroid One Rossa (as above) +- Polaroid One Ultra (silver/black) (Close focus to 2 feet) +- Polaroid Pop Kit (silver/black with stickers for user's customization) + +# Reference + +* [Polaroid One 600 Camera Review - by Dan Finnen](https://danfinnen.com/review/polaroid-one-600-camera-review/) +* [Polaroid One600 (Classic) - Camera-wiki.org - The free camera encyclopedia](http://camera-wiki.org/wiki/Polaroid_One600_(Classic)) diff --git a/content/Photography/Cameras_Research/Polaroid/attachments/Pasted image 20230330195031.png b/content/Photography/Cameras_Research/Polaroid/attachments/Pasted image 20230330195031.png new file mode 100644 index 000000000..04da89d18 Binary files /dev/null and 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a/content/Photography/MoodBoard/Sea_20230428/attachments/shiifoncake_339164445_155642070453847_6842139942547564019_n.jpg b/content/Photography/MoodBoard/Sea_20230428/attachments/shiifoncake_339164445_155642070453847_6842139942547564019_n.jpg new file mode 100644 index 000000000..a8a8e5534 Binary files /dev/null and b/content/Photography/MoodBoard/Sea_20230428/attachments/shiifoncake_339164445_155642070453847_6842139942547564019_n.jpg differ diff --git a/content/Photography/MoodBoard/Sea_20230428/idea.md b/content/Photography/MoodBoard/Sea_20230428/idea.md new file mode 100644 index 000000000..d572a5e96 --- /dev/null +++ b/content/Photography/MoodBoard/Sea_20230428/idea.md @@ -0,0 +1,45 @@ +--- +title: idea - reference image +tags: +- photography +- moodboard +- idea +--- + +# [Fujifilm_Blue_by_小红书_Philips谢骏](Photography/Aesthetic/Landscape/Sea/Fujifilm_Blue_by_小红书_Philips谢骏.md) + +![](Photography/Aesthetic/Landscape/Sea/attachments/Pasted%20image%2020230420014349.png) + + +![](Photography/Aesthetic/Landscape/Sea/attachments/Pasted%20image%2020230420014354.png) + + +![](Photography/Aesthetic/Landscape/Sea/attachments/Pasted%20image%2020230420014401.png) + + +![](Photography/Aesthetic/Landscape/Sea/attachments/Pasted%20image%2020230420014613.png) + + +![](Photography/Aesthetic/Landscape/Sea/attachments/Pasted%20image%2020230420014622.png) + + +![](Photography/Aesthetic/Landscape/Sea/attachments/Pasted%20image%2020230420014634.png) + +# [豊島_Instagram_shiifoncake](Photography/Aesthetic/Landscape/Sea/豊島_Instagram_shiifoncake.md) + +![](Photography/MoodBoard/Sea_20230428/attachments/shiifoncake_338949220_771246770941652_287141902256013940_n.jpg) + +![](Photography/MoodBoard/Sea_20230428/attachments/shiifoncake_339164445_155642070453847_6842139942547564019_n%20(1).jpg) + +![](Photography/MoodBoard/Sea_20230428/attachments/shiifoncake_339164445_155642070453847_6842139942547564019_n.jpg) + +![](Photography/MoodBoard/Sea_20230428/attachments/shiifoncake_338803198_1141886276488589_5464974698780309052_n%20(1).jpg) + +![](Photography/MoodBoard/Sea_20230428/attachments/shiifoncake_338803198_1141886276488589_5464974698780309052_n.jpg) + +![](Photography/MoodBoard/Sea_20230428/attachments/shiifoncake_338758486_601356648715316_3737336679741136784_n.jpg) + + +# [寄り道の理由。- Instagram, photono_gen](https://www.instagram.com/p/CrVPFjZvvlr/) + +![](Photography/MoodBoard/Sea_20230428/attachments/photono_gen_336060179_2380745882102401_2427706248624984378_n.jpg) \ No newline at end of file diff --git a/content/Photography/Photography_MOC.md b/content/Photography/Photography_MOC.md new file mode 100644 index 000000000..a46558748 --- /dev/null +++ b/content/Photography/Photography_MOC.md @@ -0,0 +1,80 @@ +--- +title: "Photography - MOC" +tags: +- MOC +- photography +--- + +# 🌊Photo Portfolio +You can see my photography works in: + +* [🎨Slide show](https://pinkr1ver.com/PhotoGallery/) +* [🌄Photo Collection in Notion](https://pinkr1ver.notion.site/3cfdd332b9a94b20bca041f2aa2bdcd2?v=24e696e6ab754386a710bc8e83976357&pvs=4) +* [🍻Instagram](https://www.instagram.com/jude.wang.yc/?next=%2F) +* [🧶小红书](https://www.xiaohongshu.com/user/profile/6272c025000000002102353b) + +# Notes +Also, here's my notes about learning photography + +## About Basic Concepts: + +* [Saturation](Photography/Basic/Saturation.md) + +## Appreciation of other works - about ***aesthetic*** + +* [👧Portrait](Photography/Aesthetic/Portrait/Portrait_MOC.md) +* [🏔Landscape](Photography/Aesthetic/Landscape/Landscape_MOC.md) +* [☝Style](Photography/Aesthetic/Style/Style_MOC.md) +* [✨Polaroid](Photography/Aesthetic/Polaroid/Polaroid_aesthetic_MOC.md) + +## Camera Research + +* [✨Polaroid](Photography/Cameras_Research/Polaroid/Polaroid.md) +* [📷Lens Structure](Photography/Cameras_Research/Lens_Structure/Lens_Structure_MOC.md) +* [📸Pocket film camera](Photography/Cameras_Research/Pocket_film/Pocket_film_camera_MOC.md) + +## Skills I learned + +* [How to measure light using Polaroid?](Photography/Skills/Polaroid_light.md) +* [How to use Moodboard](Photography/Skills/Moodboard.md) +* [How to show your Polaroid Picture](Photography/Aesthetic/Polaroid/Polaroid_showcase.md) + +## Photography story + +* [夜爬蛤蟆峰拍Polaroid慢门 - 2023.04.14](Photography/Story/Rainy_evening_hiking_Polaroid.md) + +## Mood Board + +* [🌊Sea - 2023.04.28](Photography/MoodBoard/Sea_20230428/Sea_20230428.md) + +## Meme + +* [Photography meme](Photography/Photography_meme/Photography_meme.md) + + +# Reference + +## Platform + +* [Magnum Photos](https://www.magnumphotos.com/) +* [CNU - Catch Next Ultimate](http://www.cnu.cc/) + +## Greatest Artist + +* [linksphotograph](https://www.linksphotograph.com/) +* [HAMADA Hideaki / 濱田英明](https://www.hideakihamada.com) +* [Jason Kummerfeldt](https://graincheck.darkroom.com/) and [his youtube](https://www.youtube.com/@grainydaysss) +* [Nguan](https://nguan.tv/) +* [Marta Bevacqua](https://www.martabevacquaphotography.com/) +* [Sam Zhang](https://www.instagram.com/itscapturedbysam/) + +## Content Collector & Photographer + +* [🦺搬运UP主 - 豆腐素包](https://space.bilibili.com/196700312/video) +* [小八怪 - 小红书](https://www.xiaohongshu.com/user/profile/5558b47f5894463d532a632c) + + +# Photography Resume + + + diff --git a/content/Photography/Photography_meme/Photography_meme.md b/content/Photography/Photography_meme/Photography_meme.md new file mode 100644 index 000000000..8b44827a7 --- /dev/null +++ b/content/Photography/Photography_meme/Photography_meme.md @@ -0,0 +1,10 @@ +--- +title: Photography Meme +tags: + - photography + - meme + - film + - happy +--- + +![](Photography/Photography_meme/attachments/QQ图片20230424193512.png) \ No newline at end of file diff --git a/content/Photography/Photography_meme/attachments/QQ图片20230424193512.png 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+使用[Adobe Color](https://color.adobe.com/)确定色彩方案 + + +# 服装道具 + +略 + +# 模特 + +略 + +# 场地 + +略 + +# 构图 + +使用参考图和手绘 + +# 布光 + +略 + +# Reference + +* [要做出完美的拍摄策划，必须知道的8个重点 - 小红书, Tripitaka Wu](https://www.xiaohongshu.com/user/profile/6272c025000000002102353b/62024914000000002103cedf) \ No newline at end of file diff --git a/content/Photography/Skills/Polaroid_light.md b/content/Photography/Skills/Polaroid_light.md new file mode 100644 index 000000000..c22997763 --- /dev/null +++ b/content/Photography/Skills/Polaroid_light.md @@ -0,0 +1,22 @@ +--- +title: How to measure light using Polaroid? +tags: +- photography +- Polaroid +- film +- skill +--- + +The most thing you need to know is that, **the right exposure is in your head**. + +# Basic + + + +# Practice + + +# Reference + +* [How to EXPOSE your POLAROID PICTURE - Youtuber Analog Things](https://www.youtube.com/watch?v=iqU5YRG8WiE) + diff --git a/content/Photography/Skills/howToShowPolaroid.md b/content/Photography/Skills/howToShowPolaroid.md new file mode 100644 index 000000000..6edea8f3e --- /dev/null +++ b/content/Photography/Skills/howToShowPolaroid.md @@ -0,0 +1,9 @@ +--- +title: How to Show Polaroid? +tags: + - Polaroid + - photography + - skill +--- + +* [宝丽来翻拍9宫格](Photography/Aesthetic/Polaroid/Polaroid_showcase.md) \ No newline at end of file diff --git a/content/Photography/Story/Rainy_evening_hiking_Polaroid.md b/content/Photography/Story/Rainy_evening_hiking_Polaroid.md new file mode 100644 index 000000000..9b2ac54b0 --- /dev/null +++ b/content/Photography/Story/Rainy_evening_hiking_Polaroid.md @@ -0,0 +1,80 @@ +--- +title: 夜爬蛤蟆峰拍Polaroid慢门 - 2023.04.14 +tags: +- photography +- Polaroid +- story +- film +--- + +# Hiking + +周五，周潭来杭，计划去蛤蟆峰顶拍拍立得慢门，记录西湖夜景。 + +晚饭后，雨渐起，兴致不减，亦去。 + +山底已经在小雨中颇有丁达尔现象的感觉。 + +![](Photography/Story/attachments/9970714720C0835E6547C263418D551B.jpg) + +雨让石头逐渐变得打滑，蛤蟆峰山顶的石头快的攀登会变得非常危险，这一点难以描述，或许你可以问你杭州本地的朋友。周潭在攀登最后一段路程之前摔倒，还好背包缓冲了几乎所有的冲撞，也让他意识到雨天来到这里的危险性，是具有极限运动的底色在的。 + +最后，在小心翼翼中，登顶了。 + +# Photographer + +在蛤蟆峰顶拍慢门需要一定的三脚架架设技巧和测光技巧，在雨中就显得更加困难。 + +![](Photography/Story/attachments/QQ视频20230416012046.mp4) + +![](Photography/Story/attachments/FCB8B96468D3B459532E010E865D0B99.jpg) + + +经过测光和宝丽来app曝光调整，这次拍摄夜景的计划以$f/22$, 30s shutter speed, i-type film 640 ISO进行拍摄，先看成片效果： + +![](Photography/Story/attachments/IMG_5553.jpg) + +照片由iPhone 12 mini Polaroid app scanner扫描完成的film -> digital，效果比较一般，但我们能看出，曝光的效果不尽人意。这里的原因认为由以下原因导致： +* 天气恶劣，空气湿度大，造成光线色散加重 +* 没有考虑i-type相纸**倒易率**，曝光时间不足（重要原因🚧🚧🚧） +* 没有查询Polaroid now+镜头最好的光学素质的参数，自认为是$f/22$，导致曝光时间过长导致的点光源色散严重。（目前还没有查询到Polaroid now+镜头的光学参数曲线🚧🚧🚧） + +同时，那晚还不懂now+ +键的使用导致相纸浪费一张，下面是now+中+键的用法： + +![](Photography/Story/attachments/Pasted%20image%2020230416014050.png) + +同时，那晚曝光时，有一次光圈不小心打到$f/33$，导致欠曝地更为厉害，其效果大概如下： + +![](Photography/Story/attachments/IMG_5550.jpg) + +同时要注意的是，Polaroid的曝光时间最多是30s，如果要更长时间的曝光，可以不弹相纸进行二次曝光，但是长曝光30s以上可能效果很差。 + +## 人像 + +搞了两张人像，同样的曝光参数$f/22$, 30s shutter speed, i-type film 640 ISO，开了宝丽来闪关灯最大等级： + +![](Photography/Story/attachments/IMG_5492.jpg) + + +![](Photography/Story/attachments/IMG_5493.jpg) + +第一张人像清晰些，以我个人观点来看，是因为伞造成的反射 + +# 返程 + +返程的故事有趣了些，因为三脚架落在了山脚，于是返回去取，但是去取的时候手机落在了打的网约车上。 + +因为手机丢了，所以无法确认订单的详细信息，也就无法联系司机和客服。 + +所以用周潭的手机去登录高德打车去确认订单，但是登录高德又需要手机验证码，非常傻逼的设计就是了，还好带了apple watch，连接了周潭的热点后可以同步手机消息收到验证码，这才登上了高德地图。 + +高德地图的打车是联动多家打车公司的，所以情况错综复杂，我的订单来自天猫出行，高德端不允许我直接联系师傅，同时天猫出行的客服也无法拨通，最后还好拨通了高德客服的电话，联系上了师傅。 + +师傅当时前往了滨江，所以我们只好在山脚下，也就是保俶路的忠儿面馆那里等待，刚好周潭没有吃饱，起源巧合下，在这也算吃了一顿还算杭州特色的拌川。 + +![](Photography/Story/attachments/A9A6699D1859851AB1D66131BD1382DC.jpg) + + +# Route + +![](Photography/Story/attachments/QQ图片20230417203443.jpg) \ No newline at end of file diff --git a/content/Photography/Story/attachments/9970714720C0835E6547C263418D551B.jpg b/content/Photography/Story/attachments/9970714720C0835E6547C263418D551B.jpg 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+ + +

Jude Wang

+ +
+ diff --git a/content/Physics/Electromagnetism/Basic/Electric_units.md b/content/Physics/Electromagnetism/Basic/Electric_units.md new file mode 100644 index 000000000..8555d796b --- /dev/null +++ b/content/Physics/Electromagnetism/Basic/Electric_units.md @@ -0,0 +1,79 @@ +--- +title: Electric Units +tags: +- ciruit +- basic +- physics +- electric +--- +# Electrical impedance + +$$ +Z = \sqrt{R^2 + {(X_L-X_C)}^2} +$$ + + +* $Z$ = impedance +* $R$ = resistance +* $X_L$ = inductive reactance +* $X_C$ = capacitive reactance + +![](Physics/Electromagnetism/Basic/attachments/Pasted%20image%2020230330163734.png) + +**阻抗**是电路中电阻、电感、电容对交流电的阻碍作用的统称。阻抗是一个复数，实部称为**电阻**，虚部称为**电抗**；其中电容在电路中对交流电所起的阻碍作用称为**容抗**，电感在电路中对交流电所起的阻碍作用称为**感抗**，容抗和感抗合称为**电抗**。 + +阻抗将电阻的概念加以延伸至交流电路领域，不仅描述*电压与电流的相对振幅*，也描述其*相对相位*。当通过电路的电流是直流电时，电阻与阻抗相等，电阻可以视为相位为零的阻抗。 + +## 形式 + +1. $R+jX$ +2. $Z_m\angle\theta$ +3. $Z_m e^{j\theta}$ + +阻抗定义为电压与电流的频域比率。阻抗的大小$Z_{m}$ 是电压振幅与电流振幅的绝对值比率，阻抗的相位 $\theta$是电压与电流的相位差。 + +## 欧姆定律 + +$$ +v = iZ = iZ_m e^{j\theta} +$$ + +阻抗大小$Z_m$的作用恰巧就像电阻，设定电流$i$，就可以计算出阻抗$Z$两端的电压降$v$。相位因子$e^{j\theta}$则是电流滞后于电压的相位差$\theta$ + +> [!tip] +> 在时域中，电流信号会比电压信号慢$\theta T/2\pi$秒 + +## 理想的阻抗 +$$ +Z_R = R +$$ + +$$ +Z_C = \frac{1}{j\omega C} +$$ + +$$ +Z_L = j \omega L +$$ + +* 对于电容，交流电压滞后90°于交流电流； +* 对于电感，交流电压超前90°于交流电流 + +### 容抗 + +$$ +X_C = -j/\omega C +$$ +随着$\omega$趋向于0，电源趋向于直流电源，容抗的绝对值趋向于无穷；*因此，在低频率运作时，电容器貌似断路。假设电源的频率越高，则容抗越低，对于电流通过的阻碍也越低。在高频率运作时，电容器貌似短路。* + +### 阻抗 + +$$ +X_L = j\omega L +$$ +从这方程可以观察到，当交流电源的角频率趋向于零时，电源会趋向于直流电源，感抗会趋向于零，对于电流的通过阻碍越低。*所以，在低频率运作时，电感器貌似短路。假设电源角频率越高，则感抗越高，假设给定电压源振幅，则电流会趋向于零。所以，在高频率运作时，电感器貌似断路。* + + +# Reference + +[电气单位（V，A，Ω，W，...） (rapidtables.org)](https://www.rapidtables.org/zh-CN/electric/Electric_units.html) diff --git a/content/Physics/Electromagnetism/Basic/attachments/Pasted image 20230330163734.png b/content/Physics/Electromagnetism/Basic/attachments/Pasted image 20230330163734.png new file mode 100644 index 000000000..054eac17d Binary files /dev/null and b/content/Physics/Electromagnetism/Basic/attachments/Pasted image 20230330163734.png differ diff --git a/content/Physics/Electromagnetism/Basic/attachments/Pasted image 20230330165822.png b/content/Physics/Electromagnetism/Basic/attachments/Pasted image 20230330165822.png new file mode 100644 index 000000000..b6890fdb5 Binary files /dev/null and b/content/Physics/Electromagnetism/Basic/attachments/Pasted image 20230330165822.png differ diff --git a/content/Physics/Electromagnetism/Electromagnetism_MOC.md b/content/Physics/Electromagnetism/Electromagnetism_MOC.md new file mode 100644 index 000000000..81d7a5e27 --- /dev/null +++ b/content/Physics/Electromagnetism/Electromagnetism_MOC.md @@ -0,0 +1,19 @@ +--- +title: Electromagnetism MOC +tags: +- physics +- MOC +- electromagnetism +--- + +# Basic + +* [Electric units](Physics/Electromagnetism/Basic/Electric_units.md) + +## Advanced + +* [Maxwell's equation](Physics/Electromagnetism/Maxwells_equation.md) + +# Circuit + +* [Resonant circuit](Physics/Electromagnetism/Resonant_circuit.md) \ No newline at end of file diff --git a/content/Physics/Electromagnetism/Maxwells_equation.md b/content/Physics/Electromagnetism/Maxwells_equation.md new file mode 100644 index 000000000..44afbad21 --- /dev/null +++ b/content/Physics/Electromagnetism/Maxwells_equation.md @@ -0,0 +1,195 @@ +--- +title: Maxwell's Equation +tags: +- physics +- electromagnetism +- nuclear-level-knowledge +--- + +# Equation + + +$$ +\nabla \cdot E = \frac{\rho}{\epsilon_0} +$$ + +$$ +\nabla \cdot B = 0 +$$ + +$$ +\nabla \times E = -\frac{\partial B}{\partial t} +$$ + +$$ +\nabla \times B = \mu_0 (J + \epsilon_0 \frac{\partial E}{\partial t}) +$$ + +# Vector field + +Essentially a vector field is what you get if you associate each point in space with a vector, some magnitude and direction. Maybe those vectors represent the velocities of particles of fluid at each point in space or maybe they represent the force of gravity at many different points in space or maybe a magnetic field strength. + +> [!note] +> If you were to draw the vectors to scale, the longer ones end up just cluttering the whole thing, so it's common to basically lie a little and artificially shorten ones that are too long. Maybe using **color to give some vague sense of length**. + +![](Physics/Electromagnetism/attachments/Pasted%20image%2020230411151612.png) + +## Divergence + +![](Physics/Electromagnetism/attachments/my-life.gif) + +Divergence $\cdot$ Vector filed是来衡量在(x, y)点你产生fluid的能力 + +所以上述图中，产生fluid的source点，他们的Divergence $\cdot$ Vector filed是positive的 + +那些fluid流入的sink端，他们的Divergence $\cdot$ Vector filed就是negative的 + +![](Physics/Electromagnetism/attachments/Pasted%20image%2020230411155711.png) + +同时，如果点可以slow flow in变fast slow out，这个点位的divergence $\cdot$ vector filed也是positive的 + +![](Physics/Electromagnetism/attachments/my-life%201.gif) + +Vector field input point得到的是一个多维的输出，指向一个方向并带有scale；divergence $\cdot$ vector field，它的输出depends on the behavior of the field in small neighborhood around that point。输出为一个数值，衡量这个point acts as a source or a sink + +![](Physics/Electromagnetism/attachments/Pasted%20image%2020230411161346.png) + +> [!note] +> For actual fluid flow: $\text{div} F = 0$ everywhere + +## Curl + +![](Physics/Electromagnetism/attachments/output%202.gif) + +Curl是衡量fluid在point被rotate的程度，clockwise方向是positive curl，counterclockwise是negative curl。 + +![](Physics/Electromagnetism/attachments/curl.gif) + +上图中这个点的curl也是非零的，因为fluid上快下慢，result in clockwise influence + +## Calculate divergence and curl + +$$ +\text{div} F = \nabla \cdot F = +\begin{bmatrix} +\frac{\partial}{\partial x} \\ +\frac{\partial}{\partial y} +\end{bmatrix} \cdot +\begin{bmatrix} +F_x \\ +F_y +\end{bmatrix} = \frac{\partial F_x}{\partial x} + \frac{\partial F_y}{\partial y} +$$ + +$$ +\text{curl} F = \nabla \times F = +\begin{bmatrix} +\frac{\partial}{\partial x} \\ +\frac{\partial}{\partial y} +\end{bmatrix} \times +\begin{bmatrix} +F_x \\ +F_y +\end{bmatrix} += \frac{\partial F_y}{\partial x} - \frac{\partial F_x}{\partial y} +$$ + +![](Physics/Electromagnetism/attachments/calculation_result.gif) + +### Detail Explanation + +![](Physics/Electromagnetism/attachments/Pasted%20image%2020230412144351.png) + +![](Physics/Electromagnetism/attachments/Pasted%20image%2020230412144501.png) + +在$(x_0, y_0)$微分一个很小的tiny step，会有一个新的vector，它与原有的vector会有一个difference。 + +![](Physics/Electromagnetism/attachments/div.gif) + +$\text{div} F(x_0, y_0)$其实就是corresponds to $360^\circ$方向的average的Step $\cdot$ Difference + +可以想象一个source端，它朝四面发射vector，它的Step $\cdot$ Difference自然就是positive的 + +![](Physics/Electromagnetism/attachments/Pasted%20image%2020230412145732.png) + +同理，不难想象的是，$\text{curl} F(x_0, y_0)$是corresponds to Step $\times$ Difference + +# Understand Maxwell's Equation + +学会vector filed中的divergence和curl，是理解Maxwell’s Equation的关键 + +## Gauss's Law + +$$ +\text{div} E = \frac{\rho}{\epsilon_0} +$$ + + +![](Physics/Electromagnetism/attachments/Pasted%20image%2020230411163735.png) + +* $\rho$是charge density +* $\epsilon_0$是Epsilon Naught，free space的介电常数，它决定free space空间中电场的强度 + +> [!note] +> 形象的 +> +> Gauss's law stating that **divergence of an electric field at a given point is a proportional to the charge density at that point**. +> +> **Positively charged regions as acting like sources** of some imagined fluid and n**egatively charged regions as being the sinks** of that fluid. +> +> Parts of space where there is on charge the fluid **would be flowing incompressively** just like water. + + +## Gauss's law for magnetism + +$$ +\text{div} B = 0 +$$ + +![](Physics/Electromagnetism/attachments/Pasted%20image%2020230411165048.png) + +磁场的divergence在任意地方为0，说明磁场的fluid是incompressible的，没有source也没有sinks，就像water一样。也有这样的interpretation，说明magnetic monopoles是不存在的 + +## Maxwell–Faraday equation (Faraday's law of induction) + +$$ +\nabla \times E = - \frac{1}{c} \frac{\partial B}{\partial t} +$$ + +![](Physics/Electromagnetism/attachments/Pasted%20image%2020230419141438.png) + +![](Physics/Electromagnetism/attachments/Pasted%20image%2020230419141637.png) +## Ampère's circuital law (with Maxwell's addition) + +$$ +\nabla \times B = \frac{1}{c} (4\pi J + \frac{\partial E}{\partial t}) +$$ + +![](Physics/Electromagnetism/attachments/Pasted%20image%2020230419141737.png) + + +# Maxwells equation explain EM wave + +Maxwells的完备对称理论表明，电场力和磁力并不是分开的，而是同一事物——电磁力的不同表现形式。 这种力的经典统一是当前试图统一自然界中四种基本力——引力、电力、强核力和弱核力——的动机之一。 + +Maxwells从Maxwells equation中预测了EM wave的存在。 + +Maxwells意识到振荡电荷，就像交流电路中的电荷一样，会产生变化的电场。 他预测这些变化的场会像跳跃的鱼在湖上产生的波浪一样从源头传播。 + +麦克斯韦预测的波将由振荡电场和磁场组成——定义为电磁波（EM 波）。 电磁波能够对距其源很远的电荷施加力，因此它们可能是可检测的。 Maxwells通过求解Maxwells方程组，可以求出EM的速度$c$， + +$$ +c = \frac{1}{\sqrt{\mu_0 \epsilon_0}} = 3 \times 10^8 m/s +$$ + +电磁波的波段处于无法被肉眼观测的波段，直到Maxwells去世后，才被Hertz用实验证实了电磁波的存在。 + +![](Physics/Electromagnetism/attachments/Pasted%20image%2020230419155744.png) + +# Reference + +* [Fun fluid-flow illustrations - by 3B1B](https://anvaka.github.io/fieldplay/?cx=0&cy=0&w=8.5398&h=8.5398&dt=0.01&fo=0.998&dp=0.009&cm=1&vf=%2F%2F%20p.x%20and%20p.y%20are%20current%20coordinates%0A%2F%2F%20v.x%20and%20v.y%20is%20a%20velocity%20at%20point%20p%0Avec2%20get_velocity%28vec2%20p%29%20%7B%0A%20%20vec2%20v%20%3D%20vec2%280.%2C%200.%29%3B%0A%0A%20%20%2F%2F%20change%20this%20to%20get%20a%20new%20vector%20field%0A%20%20v.x%20%3D%20p.y%3B%0A%20%20v.y%20%3D%20%28max%28cos%28sin%28p.y%29%29%2Csin%28p.y%29%2Fp.y%29%2Bp.y%29%3B%0A%0A%20%20return%20v%3B%0A%7D&code=%2F%2F%20p.x%20and%20p.y%20are%20current%20coordinates%0A%2F%2F%20v.x%20and%20v.y%20is%20a%20velocity%20at%20point%20p%0Avec2%20get_velocity%28vec2%20p%29%20%7B%0A%20%20vec2%20v%20%3D%20vec2%280.%2C%200.%29%3B%0A%0A%20%20%2F%2F%20change%20this%20to%20get%20a%20new%20vector%20field%0A%20%20v.x%20%3D%20%28max%28p.x%2Cp.y%29%2Bmax%28p.y%2Cp.x%29%29%3B%0A%20%20v.y%20%3D%20p.y%3B%0A%0A%20%20return%20v%3B%0A%7D) +* [Divergence and curl: The language of Maxwell's equations, fluid flow, and more - YouTube vedio by 3b1b](https://www.youtube.com/watch?v=rB83DpBJQsE) +* [Let There Be Light: Maxwell's Equation EXPLAINED for BEGINNERS - YouTube vedio by Parth G](https://www.youtube.com/watch?v=0jW74lrpeM0) +* [Faraday’s Law - online experiment](https://em.geosci.xyz/content/maxwell1_fundamentals/formative_laws/faraday.html) +* [# Maxwell’s Equations- Electromagnetic Waves Predicted and Observed](https://phys.libretexts.org/Bookshelves/College_Physics/Book%3A_College_Physics_1e_(OpenStax)/24%3A_Electromagnetic_Waves/24.01%3A_Maxwells_Equations-_Electromagnetic_Waves_Predicted_and_Observed) \ No newline at end of file diff --git a/content/Physics/Electromagnetism/Q_factor.md b/content/Physics/Electromagnetism/Q_factor.md new file mode 100644 index 000000000..d99286605 --- /dev/null +++ b/content/Physics/Electromagnetism/Q_factor.md @@ -0,0 +1,62 @@ +--- +title: Q factor +tags: +- physics +- electric +- electromagnetism +- basic +--- + +# Explanation + +In physics and engineering, the quality factor or Q factor is a **dimensionless** parameter that describes how **underdamped** an oscillator or *resonator* is. It is defined as the ratio of the initial energy stored in the resonator to the *energy lost* in one radian of the cycle of oscillation. Q factor is alternatively defined as the ratio of a *resonator's center frequency to its bandwidth* when subject to an oscillating driving force. These two definitions give *numerically similar*, but not identical, results. + +> [!tip] +> 高Q因子表示振子能量损失的速率较慢，振动可持续较长的时间; 单摆在空气中Q因子较高而在油中较低 + + + +![](Physics/Electromagnetism/attachments/Pasted%20image%2020230404144801.png)Fig. A damped oscillation. A low Q factor – about 5 here – means the oscillation dies out rapidly. + + +Q因子较高的振子在共振时，在共振频率附近的**振幅较大**，但会产生的共振的**频率范围比较小**，此频率范围可以称为频宽。 + +例如一台无线电接收器内的调谐电路Q因子较高，要调整接收器对准一特定频率会比较困难，但其选择性较好，在过滤频谱上邻近电台的讯号上也有较佳的效果。 + +系统的Q因子可能会随著应用场合及需求的不同而有大幅的差异。*强调阻尼特性的系统*（例如[防止门突然关闭的阻尼器](warehouse/dampers_keeping_a_door_from_slamming%20shut.md)）*其Q因子为1⁄2*，而时钟、雷射或是其他需要强烈共振或是要求频率稳定性的系统其Q因子也较高。音叉的Q因子大约为1000，原子钟、加速器中的超导射频或是光学共振腔的Q因子可以到$10^{11}$ + +> [!help] +> There are many *alternative quantities* used by physicists and engineers to describe how damped an oscillator is. Important examples include: the [damping ratio](https://en.wikipedia.org/wiki/Damping_ratio "Damping ratio"), [relative bandwidth](https://en.wikipedia.org/wiki/Bandwidth_(signal_processing) "Bandwidth (signal processing)"), [linewidth](https://en.wikipedia.org/wiki/Oscillator_linewidth "Oscillator linewidth") and bandwidth measured in [octaves](https://en.wikipedia.org/wiki/Octave_(electronics) "Octave (electronics)"). + + +# Definition + +![](Physics/Electromagnetism/attachments/Pasted%20image%2020230404151254.png) + +Fig. 一阻尼谐振子的频宽, $\Delta f$可以用频率和能量的图来表示。阻尼谐振子（或滤波器）的Q因子为$f_{0}/\Delta f$。Q因子越大，其波峰高度会越高，而其宽度会越窄 + +In the context of resonators, there are two common definitions for Q, which aren't exactly equivalent. They become approximately equivalent *as Q becomes larger*, meaning the resonator becomes less damped. + +## Bandwidth definition + +$$Q\stackrel{def}{=}\frac{f_r}{\Delta f}=\frac{\omega_r}{\Delta \omega}$$ + +$f_r$为共振频率，$\Delta f$为频宽，一般是 [full width at half maximum](https://en.wikipedia.org/wiki/Full_width_at_half_maximum "Full width at half maximum") (FWHM) + +## Stored energy definition + +Q因子可定义为在一系统的共振频率下，当信号振幅不随时间变化时，**系统储存能量和每个周期外界所提供能量的比例**（此时系统储存能量也不随时间变化） + +$$Q = 2\pi \times \frac{\text{Energy Stored}}{\text{Energy dissipated per cycle}}=2\pi f_r \times \frac{\text{Energy Stored}}{\text{Power Loss}}$$ + +同时在像电感等储能元件的规格中，会用到和频率有关的Q因子，其定义如下 + +$$Q(\omega) = \omega \times \frac{\text{Maximum Energy Stored}}{\text{Power Loss}}$$ + +其中$\omega$是计算储存能量和功率损失时的角频率 + + +# Reference + +* [Q factor in wiki](https://en.wikipedia.org/wiki/Q_factor) +* [品质因子](https://zh.wikipedia.org/zh-hans/%E5%93%81%E8%B3%AA%E5%9B%A0%E5%AD%90#:~:text=%E5%93%81%E8%B4%A8%E5%9B%A0%E5%AD%90%E6%88%96Q%E5%9B%A0%E5%AD%90,%E6%91%86Q%E5%9B%A0%E5%AD%90%E8%BE%83%E4%BD%8E%E3%80%82) \ No newline at end of file diff --git a/content/Physics/Electromagnetism/Resonant_circuit.md b/content/Physics/Electromagnetism/Resonant_circuit.md new file mode 100644 index 000000000..1eed506ef --- /dev/null +++ b/content/Physics/Electromagnetism/Resonant_circuit.md @@ -0,0 +1,52 @@ +--- +title: Resonant circuit +tags: +- physics +- electric +--- + +以RLC串联电路为例 + +# 什么是谐振 + +电路中电容器$L$、电感器$C$两组件之能量相等，当能量由电路中某一电抗组件释出时，且另一电抗组件必吸收相同之能量，即此两电抗组件间会产生一能量脉动。 + +# 两种简单的谐振电路 +![](synthetic_aperture_radar_imaging/attachments/Pasted%20image%2020230330160535.png) + + +以串联谐振为例 + +## *Resonant Frequency* + +电容，电阻的[电抗](Physics/Electromagnetism/Basic/Electric_units.md#Electrical%20impedance)相同时发生谐振 + +$$ +|X_C| = |\frac{1}{j2\pi fC}| = |X_L| = |j2\pi fL| +$$ +Rearranging, + +$$ +f^2 = \frac{1}{(2\pi)^2 C L} +$$ + +$$ +f = \frac{1}{2\pi \sqrt{LC}} +$$ + +## 串联谐振特性 + +* 阻抗最小，且为纯电阻，$Z = R+jXL-jXC = R$ + +## **品质因子** ([*Q factor*](Physics/Electromagnetism/Q_factor.md)) + +* 电感器或电容器在谐振时产生的电抗功率与电阻器消耗的平均功率之比，称为谐振时之品质因子。 + +$$Q=\frac{Q_L}{P}=\frac{I^2X_L}{I^2R}=\frac{Q_C}{P}=\frac{I^2X_C}{I^2R}=\frac{1}{R}\sqrt{\frac{L}{C}}=\frac{\sqrt{X_LX_C}}{R}$$ + +#### 阻抗与频率的关系 + +$Z = R + j(X_L-X_C)$ +* 当$f＝f_r$时，$Z＝R$为最小值，电路为电阻性； +* 当$f＞f_r$时，$X_L＞X_C$为最小值，电路为电感性； +* 当$f＜f_r$时，$X_L＜X_C$为最小值，电路为电容性。 diff --git a/content/Physics/Electromagnetism/attachments/Pasted image 20230404144801.png b/content/Physics/Electromagnetism/attachments/Pasted image 20230404144801.png new file mode 100644 index 000000000..7b426ca60 Binary files /dev/null and b/content/Physics/Electromagnetism/attachments/Pasted image 20230404144801.png differ diff --git a/content/Physics/Electromagnetism/attachments/Pasted image 20230404151254.png b/content/Physics/Electromagnetism/attachments/Pasted image 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