Time Dilation 时间膨胀

In physics and relativity, Time Dilation is the difference in the elapsed time as measured by two clocks. It is either due to a relative velocity between them (“kinetic” time dilation, from special relativity) or to a difference in gravitational potential between their locations (gravitational time dilation, from general relativity). When unspecified, “time dilation” usually refers to the effect due to velocity. After compensating for varying signal delays due to the changing distance between an observer and a moving clock (i.e. Doppler effect), the observer will measure the moving clock as ticking slower than a clock that is at rest in the observer’s own reference frame. In addition, a clock that is close to a massive body (and which therefore is at lower gravitational potential) will record less elapsed time than a clock situated further from the said massive body (and which is at a higher gravitational potential). These predictions of the theory of relativity have been repeatedly confirmed by experiment, and they are of practical concern, for instance in the operation of satellite navigation systems such as GPS and Galileo. High-accuracy timekeeping, low-Earth-orbit satellite tracking, and pulsar timing are applications that require the consideration of the combined effects of mass and motion in producing time dilation. Practical examples include the International Atomic Time standard and its relationship with the Barycentric Coordinate Time standard used for interplanetary objects. Relativistic time dilation effects for the solar system and the Earth can be modeled very precisely by the Schwarzschild solution to the Einstein field equations. In the Schwarzschild metric, the interval $d t_{\mathrm{E}}$ is given by: $$d t_{\mathrm{E}}^{2}=\left(1-\frac{2 G M_{\mathrm{i}}}{r_{\mathrm{i}} c^{2}}\right) d t_{\mathrm{c}}^{2}-\left(1-\frac{2 G M_{\mathrm{i}}}{r_{\mathrm{i}} c^{2}}\right)^{-1} \frac{d x^{2}+d y^{2}+d z^{2}}{c^{2}}$$ where: $d t_{\mathrm{E}}$ is a small increment of proper time $t_{\mathrm{E}}$ (an interval that could be recorded on an atomic clock),$d t_{\mathrm{c}}$ is a small increment in the coordinate $t_{\mathrm{c}}$ (coordinate time),dx, dy, dz are small increments in the three coordinates x, y, z of the clock’s position,$\frac{-G M_{i}}{r_{i}}$ represents the sum of the Newtonian gravitational potentials due to the masses in the neighborhood, based on their distances ${r_{i}}$ from the clock. This sum includes any tidal potentials. The coordinate velocity of the clock is given by: $$v^{2}=\frac{d x^{2}+d y^{2}+d z^{2}}{d t_{\mathrm{c}}^{2}}$$ The coordinate time $t_{\mathrm{c}}$ is the time that would be read on a hypothetical “coordinate clock” situated infinitely far from all gravitational masses (U=0), and stationary in the system of coordinates (v=0). The exact relation between the rate of proper time and the rate of coordinate time for a clock with a radial component of velocity is: $$\frac{d t_{\mathrm{E}}}{d t_{\mathrm{c}}}=\sqrt{1+\frac{2 U}{c^{2}}-\frac{v^{2}}{c^{2}}+\left(\frac{c^{2}}{2 U}+1\right)^{-1} \frac{v_{\text {॥ }}^{2}}{c^{2}}}=\sqrt{1-\left(\beta^{2}+\beta_{e}^{2}+\frac{\beta_{\text {॥ }}^{2} \beta_{e}^{2}}{1-\beta_{e}^{2}}\right)}$$ where: $v_{\text {॥ }}^{2}$ is the radial velocity,$v_{e}=\sqrt{\frac{2 G M_{i}}{r_{i}}}$ is the escape speed,$\beta=v / c$, $\beta_{e}=v_{e} / c$, $\beta_{\text {॥ }}=v_{\text {॥ }} / c$ are velocities as a percentage of speed of light c,$U=\frac{-G M_{i}}{r_{i}}$ is the Newtonian potential; hence -U equals half the square of the escape speed. The above equation is exact under the assumptions of the Schwarzschild solution. It reduces to velocity time dilation equation in the presence of motion and absence of gravity, i.e. $\beta_{e}=0$. It reduces to gravitational time dilation equation in the absence of motion and presence of gravity, i.e. $\beta=0=\beta_{\text {॥ }}$.

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Martian 火星人

MarsLink.in 2024, LandingFive starships land on Mars, marking the beginnings of the Mars colony.All of the martian rovers sent by different countries before this day.Watch as the five uncrewed starships land and deliver life support systems,these pioneering starships pave the way for humans to land on Mars in two years time, for fishes to be grown in nine years, and for the first baby to be born on the red planet in 15 years time. 27 April 2025, Location: Erebus MontesThe five starships land at Erebus Montes.The cargo ships are delivering essential life support systems.These are made up of solar panels backup fuel, oxygen, water, dried food,waste management systems, spacesuits, medical supplies and the first habitation pods.There are also tools and equipment for experiments. One of the starships is carrying Mars’s new starlink communications network, and deploys it in orbit before landing to deliver life-support cargo. Only four satellites are needed to create the martian starlink, as the Mars base will be concentrated to one area. There are also seven football fields worth of solar panels on the cargo list.These are used to power the future base and fuel production solar panels on Mars are only 43% as efficient as they are on earth. Rovers as well as robotic dogs by Boston Dynamics which SpaceX uses to inspect rockets on earth are deployed from the starships to the martian surface. Work begins on setting up the Mars base, the rovers and robots deploy the solar arrays, prep work begins for fuel production experiments, rovers begin drilling for icy water deposits. The saboteer process is used to take the CO² from the martian atmosphere and hydrogen from mining martian icy water, and then uses heat and pressure to turn it into water oxygen and methane fuel. Multi-use rovers begin flattening and melting the martian regolith the loose soil to prepare a large flat landing pad it reduces the kick-up of dirt and rocks, increasing the safety for the next landings. The population on Mars is made up entirely of robots two years and two months have passed since the first landings of the five cargo starships and the new launch window opens as earth and Mars are close together again.

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Butterfly Effect 蝴蝶效应

The butterfly effect is the idea that small, seemingly trivial events may ultimately result in something with much larger consequences – in other words, they have non-linear impacts on very complex systems. For instance, when a butterfly flaps its wings in India, that tiny change in air pressure could eventually cause a tornado in Iowa. The term “butterfly effect” was coined in the 1960s by Edward Lorenz, a meteorology professor at the Massachusetts Institute of Technology, who was studying weather patterns. He devised a model demonstrating that if you compare two starting points indicating current weather that are near each other, they’ll soon drift apart – and later, one area could wind up with severe storms, while the other is calm. Later, other scientists realized the importance of Lorenz’s discovery. His insights laid the foundation for a branch of mathematics known as chaos theory, the idea of trying to predict the behavior of systems that are inherently unpredictable. You can see instances of the butterfly effect every day. Weather’s just one example. Climate change is another. Because, as it turns out, warming climates are impacting – appropriately enough – species of alpine butterflies in North America. 蝴蝶效应是混沌学理论中的一个概念。它是指对初始条件敏感性的一种依赖现象:输入端微小的差别会迅速放大到输出端,蝴蝶效应在经济生活中比比皆是。 “蝴蝶效应”也可称“台球效应”,它是“混沌性系统”对初值极为敏感的形象化术语,也是非线性系统在一定条件(可称为“临界性条件”或“阈值条件”)出现混沌现象的直接原因。 混沌不是偶然的、个别的事件,而是普遍存在于宇宙间各种各样的宏观及微观系统的,万事万物,莫不混沌。 混沌也不是独立存在的科学,它与其它各门科学互相促进、互相依靠,由此派生出许多交叉学科,如混沌气象学、混沌经济学、混沌数学等。 混沌学不仅极具研究价值,而且有现实应用价值,能直接或间接创造财富。

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Immune System 免疫系统

The immune system is a network of biological processes that protects an organism from diseases. It detects and responds to a wide variety of pathogens, from viruses to parasitic worms, as well as cancer cells and objects such as wood splinters, distinguishing them from the organism’s own healthy tissue. Many species have two major subsystems of the immune system. The innate immune system provides a preconfigured response to broad groups of situations and stimuli. The adaptive immune system provides a tailored response to each stimulus by learning to recognize molecules it has previously encountered. Both use molecules and cells to perform their functions. Nearly all organisms have some kind of immune system. Bacteria have a rudimentary immune system in the form of enzymes that protect against virus infections. Other basic immune mechanisms evolved in ancient plants and animals and remain in their modern descendants. These mechanisms include phagocytosis, antimicrobial peptides called defensins, and the complement system. Jawed vertebrates, including humans, have even more sophisticated defense mechanisms, including the ability to adapt to recognize pathogens more efficiently. Adaptive (or acquired) immunity creates an immunological memory leading to an enhanced response to subsequent encounters with that same pathogen. This process of acquired immunity is the basis of vaccination.

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Respiratory System 呼吸系统

The respiratory system is the organs and other parts of your body involved in breathing,when you exchange oxygen and carbon dioxide. Parts of the Respiratory System Nose and nasal cavity Sinuses Mouth Throat (pharynx) Voice box (larynx) Windpipe (trachea) Diaphragm Lungs Bronchial tubes/bronchi Bronchioles Air sacs (alveoli) Capillaries How Do We Breathe?Breathing starts when you inhale air into your nose or mouth.It travels down the back of your throat and into your windpipe,which is divided into air passages called bronchial tubes. For your lungs to perform their best, these airways need to be open.They should be free from inflammation or swelling and extra mucus. As the bronchial tubes pass through your lungs,they divide into smaller air passages called bronchioles.The bronchioles end in tiny balloon-like air sacs called alveoli.Your body has about 600 million alveoli. The alveoli are surrounded by a mesh of tiny blood vessels called capillaries.Here, oxygen from inhaled air passes into your blood. After absorbing oxygen, blood goes to your heart.Your heart then pumps it through your body to the cells of your tissues and organs. As the cells use the oxygen, they make carbon dioxide that goes into your blood.Your blood then carries the carbon dioxide back to your lungs,where it’s removed from your body when you exhale. 当您将空气吸入鼻子或嘴中时,呼吸开始。 它沿着您的喉咙后部行进,进入您的气管,气管分为称为支气管的空气通道。 为了使您的肺部表现最佳,这些呼吸道需要打开。 他们应该没有发炎或肿胀和多余的黏液。 当支气管穿过肺部时,它们会分成较小的空气通道,称为细支气管。 细支气管终止于称为肺泡的微小气球状气囊。您的身体有大约6亿个肺泡。 肺泡被称为毛细血管的细小血管网包围。在这里,吸入空气中的氧气进入您的血液。 吸收氧气后,血液流到您的心脏。然后,心脏将其通过身体泵送到组织和器官的细胞。 当细胞使用氧气时,它们会产生二氧化碳,这些二氧化碳会进入您的血液。然后,血液将二氧化碳带回肺部,在呼气时将其从体内清除。

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Photonic Quantum 光量子

A photonic quantum computer could have huge advantages over its matter-based counterpart. Photons are much less prone to interact with their environment, which means they can retain their quantum state for much longer and over long distances. A photonic quantum computer could, in theory, operate at room temperature – and as a result, scale up much faster.

Of the various approaches to quantum computing, photons are appealing for their low-noise properties and ease of manipulation at the single photon level; while the challenge of entangling interactions between photons can be met via measurement induced non-linearities.

Five Elements 五行元素

Chinese people believe that we are surrounded by five energy fields or five different kinds of “Qì” (气). These are also called the “five elements” and they play an important role in all aspects of Chinese culture, including the way people eat. This theory states that if these five elements are changed or moved, this could seriously affect a person’s fate. The “five elements” (五行) are also known as the five agents, five phases, five movements, five forces, five processes, and five planets. If the concept of yīn and yáng is the center of the Chinese culture, then the theory of the “five elements” should be treated as its cornerstone.

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Predict Failure 预测失效

Maximum Normal Stress CriterionThe maximum stress criterion, also known as the normal stress, Coulomb, or Rankine criterion, is often used to predict the failure of brittle materials.The maximum stress criterion states that failure occurs when the maximum (normal) principal stress reaches either the uniaxial tension strength st, or the uniaxial compression strength sc, $$-s_{c} \lt { s_{1}, s_{2} } \lt s_{t}$$ where $s_{1}$ and $s_{2}$ are the principal stresses for 2D stress. Graphically, the maximum stress criterion requires that the two principal stresses lie within the green zone depicted below, Mohr’s TheoryThe Mohr Theory of Failure, also known as the Coulomb-Mohr criterion or internal-friction theory, is based on the famous Mohr’s Circle. Mohr’s theory is often used in predicting the failure of brittle materials, and is applied to cases of 2D stress. Mohr’s theory suggests that failure occurs when Mohr’s Circle at a point in the body exceeds the envelope created by the two Mohr’s circles for uniaxial tensile strength and uniaxial compression strength. This envelope is shown in the figure below, The left circle is for uniaxial compression at the limiting compression stress sc of the material. Likewise, the right circle is for uniaxial tension at the limiting tension stress st. The middle Mohr’s Circle on the figure (dash-dot-dash line) represents the maximum allowable stress for an intermediate stress state. All intermediate stress states fall into one of the four categories in the following table. Each case defines the maximum allowable values for the two principal stresses to avoid failure.

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Riemann Hypothesis 黎曼猜想

Riemann hypothesis, in number theory, hypothesis by German mathematician Bernhard Riemann concerning the location of solutions to the Riemann zeta function, which is connected to the prime number theorem and has important implications for the distribution of prime numbers. Riemann included the hypothesis in a paper, “Ueber die Anzahl der Primzahlen unter einer gegebenen Grösse” (“On the Number of Prime Numbers Less Than a Given Quantity”), published in the November 1859 edition of Monatsberichte der Berliner Akademie (“Monthly Review of the Berlin Academy”). Other than the “trivial zeros” along the negative real axis, all the solutions to the Riemann zeta function must lie in the critical strip of complex numbers whose real part is between 0 and 1. The Riemann hypothesis is that all these nontrivial zeros actually lie on the critical line, or $Re(S) = 1/2$. The zeta function is defined as the infinite series $$\zeta(s)=1+2^{-s}+3^{-s}+4^{-s}+\cdots$$ or, in more compact notation, $$\zeta(s)=\sum_{n=1}^{\infty} \frac{1}{n^{s}}$$ where the summation $(Σ)$ of terms for n runs from 1 to infinity through the positive integers and s is a fixed positive integer greater than 1. The zeta function was first studied by Swiss mathematician Leonhard Euler in the 18th century. (For this reason, it is sometimes called the Euler zeta function. For $ζ(1)$, this series is simply the harmonic series, known since antiquity to increase without bound — i.e., its sum is infinite.) Euler achieved instant fame when he proved in 1735 that $ζ(2) = π^{2}/6$, a problem that had eluded the greatest mathematicians of the era, including the Swiss Bernoulli family (Jakob, Johann, and Daniel). More generally, Euler discovered (1739) a relation between the value of the zeta function for even integers and the Bernoulli numbers, which are the coefficients in the Taylor series expansion of $x/(e^{x} − 1)$. (See also exponential function.) Still more amazing, in 1737 Euler discovered a formula relating the zeta function, which involves summing an infinite sequence of terms containing the positive integers, and an infinite product that involves every prime number: $$\zeta(s)=\sum_{n=1}^{\infty} \frac{1}{n^{s}}=\prod_{p} \frac{1}{1-p^{-s}}$$ Riemann extended the study of the zeta function to include the complex numbers $x + iy$, where $i = \sqrt{−1}$, except for the line $x = 1$ in the complex plane. Riemann knew that the zeta function equals zero for all negative even integers −2, −4, −6, … (so-called trivial zeros) and that it has an infinite number of zeros in the critical strip of complex numbers that fall strictly between the lines $x = 0$ and $x = 1$. He also knew that all nontrivial zeros are symmetric with respect to the critical line $x = 1/2$. Riemann conjectured that all of the nontrivial zeros are on the critical line, a conjecture that subsequently became known as the Riemann hypothesis.

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Divergence & Curl 散度和旋度

DivergenceDivergence is an operation on a vector field that tells us how the field behaves toward or away from a point. Locally, the divergence of a vector field $\vec{F}$ in $\mathbb{R}^2$ or $\mathbb{R}^3$ at a particular point $P$ is a measure of the “outflowing-ness” of the vector field at $P$.If $\vec{F}$ represents the velocity of a fluid, then the divergence of $\vec{F}$ at $P$ measures the net rate of change with respect to time of the amount of fluid flowing away from $P$ (the tendency of the fluid to flow “out of” P). In particular, if the amount of fluid flowing into $P$ is the same as the amount flowing out, then the divergence at $P$ is zero. Definition: divergence in $\mathbb{R}^3$If $\vec{F} = \langle P,Q,R \rangle$ is a vector field in $\mathbb{R}^3$ and $P_x, , Q_y,$ and $R_z$ all exist, then the divergence of $\vec{F}$ is defined by $$\begin{aligned}\operatorname{div} F &=P_{x}+Q_{y}+R_{z} \&=\frac{\partial P}{\partial x}+\frac{\partial Q}{\partial y}+\frac{\partial R}{\partial z}\end{aligned}$$ Note the divergence of a vector field is not a vector field, but a scalar function. In terms of the gradient operator $$\vec{\nabla}=\left\langle\frac{\partial}{\partial x}, \frac{\partial}{\partial y}, \frac{\partial}{\partial z}\right\rangle$$ divergence can be written symbolically as the dot product $$\operatorname{div} \vec{F}=\vec{\nabla} \cdot \vec{F}.$$ Note this is merely helpful notation, because the dot product of a vector of operators and a vector of functions is not meaningfully defined given our current definition of dot product.

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