The Science Fiction World of Xueba

All physical problems are, in the final analysis, mathematical problems.

Uh ...

In the early morning of the next day, Pang Xuelin went directly to his office and turned on the computer. Pang Xuelin said directly: "MOSS, give me the latest simulation results of the Earth's transfer orbit today, and provide the latest research on the influence of crust motion by the gravitational field of Jupiter. data!"

"Okay, Dr. Pang Xuelin, please wait!"

Within a minute, various data files appeared on the computer desktop.

MOSS is a new-generation artificial intelligence system developed by humans based on carbon-based chips. Its main body is installed in the "Pangu" supercomputer system located in the earth ’s cab, and assists the Earth ’s joint government to control the Earth ’s flight trajectory.

分 One of its avatars is located on the Navigator Space Station and is responsible for the operation of the Navigator Space Station.

As a member of the Scientific Committee, Pang Xuelin naturally has the right to mobilize MOSS to serve him.

Pang Xuelin sat in front of the computer and began to quickly browse the latest research papers related to the intersection of ground and wood.

Uh ...

"When the ground and wood meet, Jupiter's tidal force will greatly change the distribution of water and the atmosphere, but the atmosphere and ocean will not leave the earth before the impact occurs. A fluid planet, the end (near end) close to the source of gravity is subject to gravity The larger, the end (distal end) far from the source of gravity receives less gravitational force. This difference in gravitational force will lengthen the fluid planet, so the gravitational force at the proximal end will be greater, and the gravitational force at the distal end will be less, resulting in greater gravitational force. Poor, pulling the celestial body longer, until its own gravity can no longer maintain the accumulation of fluids and be pulled into fragments. This is a positive feedback process. "

"And for the earth, the ocean and the earth are very thin layers. Under the action of tidal forces, the atmosphere and the ocean will gather at both ends near / away from Jupiter, and the positive feedback process is interrupted. At this time, to Taking away the seawater and atmosphere gathered into two ridges, it is still close to the rigid Roche limit (the earth and wood meet the rigid Roche limit of 70,000 kilometers, which is less than the radius of Jupiter), and overcome the gravity of the entire earth. "

"At a distance of 100 times Jupiter's radius (7 million kilometers) from Jupiter, Jupiter's tidal force causes a tide of several meters high."

"At a distance of 20 times Jupiter's radius (1.4 million kilometers), if the ocean is not frozen, the earth's tidal height can reach hundreds of meters, and disasters will begin to hit. The two latitude bands facing Jupiter and back to Jupiter bear the brunt. At the same time, some Earthquakes will be induced. "

"At a distance of 8 times the radius of Jupiter (560,000 kilometers). Atmospheric tides are sufficient to reduce the pressure in most parts of the earth to a level that can cause a plateau response. At the same time, the stress in the plate is exhausted, but stabilizes. The plate Volcanic activity in the intersecting areas continues to be active. "

"When approaching the earth-moon distance (300,000 kilometers), Jupiter's tidal force reaches three-thousandths of gravity, and the part of the crust at the plate boundary is getting larger and larger."

"When it is one Earth diameter (12,000 kilometers) from Jupiter, Jupiter's tidal force reaches 28% of Earth's gravity, and the crust is massively broken. The earth's tidal force is enough to capture Jupiter's atmosphere ... Perhaps it is more accurate to say-- The first wave of Jupiter's atmosphere began to hit the Earth. The Earth and Jupiter's atmosphere hit at a speed of 60 kilometers per second. This speed was much faster than the speed of sound. Energy could not escape in the form of sound waves. The atmosphere of Jupiter rushed to the Earth in succession. , Being continuously compressed, warmed, and plasmatized. "

Uh ...

有点 "It's interesting, this paper actually described the whole process of ground impact."

Pang Xuelin attached this article to his own opinion and forwarded it to the administrative secretary. Such papers have certain reference value for how the coalition government can deal with the crisis that may arise from the intersection of land and wood.

Then, he opened another file and started again, facing the complex system of nonlinear partial differential equations on the computer screen.

组 This set of non-linear partial differential equations combines the strengths of global mathematicians. The earth-wood transfer orbit equations, which are modified daily based on the latest supercomputing simulation results, are extremely computationally expensive and can only be simulated by computers.

In theory, if you want to calculate the safe transfer orbit at the intersection of ground and wood, it is only a Newtonian mechanical problem. According to the system's motion equation and initial conditions, you can determine the evolution of the system and predict the future, which belongs to the deterministic system.

实际上 But in fact, due to too many external random factors, even small changes may have a significant impact on the results.

For example, Jupiter's gravity caused turbulence in the crust, which caused a strong global earthquake, which in turn caused the planetary engine to lose thrust.

For another example, the density of Jupiter due to the gravitational problem of the earth causes a change in density, which affects the gravitational force between the two.

In addition, of the 72 Jupiter satellites, there are four satellites over 2500 kilometers in diameter, of which Europa reaches 4800 kilometers, second only to the moon. The existence of these satellites will also have gravitation to the earth. Disturb.

这些 When all these external factors are superimposed, and then the nonlinear partial differential equations are listed, it is almost impossible to give an accurate analytical solution.

In recent years, under the principle of homogeneous equilibrium, the mathematical community has developed a variety of methods for exact solutions of nonlinear partial differential equations: like Tanh-function method, Sine-Cosine method, elliptic function expansion method, equation method, and F- expansion method. , And then solve it with the help of a computer.

凭借 But by virtue of a pure mathematician's intuition, Pang Xuelin faintly felt that the method used by the mathematical community for the partial differential equations in front of him is currently limited in accuracy.

The main reason is that there are too many variables in this set of equations, and any small deviation may cause a large difference in results.

不 "No, even if you can't give an analytical solution to this set of equations, you have to give a few specific exact solutions!"

Pang Xuelin's eyes narrowed slightly.

"But which method should be used to solve it?"

Wu Pang Xuelin frowned.

"Is it possible to try to use the AC = BD mode in differential geometry and the Wu differential characterization method to give solutions of the general form of the equation in multiple forms, and then give mechanized methods for solving solitary wave solutions of nonlinear partial differential equations ... "

"No, although this method can transform the solution of nonlinear differential equations into the solution of nonlinear over-determined algebraic equations, and establish a bridge between Wu's method and the solution of differential equations. However, the variables of the equations are uncertain. The results are also less accurate! "

Uh ...

那么 "Will it be possible to use geometric integration methods to deal with this partial differential equation?"

省 One of the greatest geographers of the 20th century, Chen Shengshen once expressed the view that "the essence of physics is geometry!"

Newton's basic formula F = ma, F on the left is force, which represents physics, a on the right is acceleration, which is mathematically the second derivative, which is the curvature in geometry.

Einstein's equation Rik-1 / 2GikR = 8πKTik.

On the right is the energy-stress tensor, which belongs to physics. On the left are the Ricci curvature Rik and the scalar curvature R, which are geometry.

Yang Zhenning's gauge field theory is essentially fiber bundle geometry.

几何 It is not uncommon to use geometric methods to solve nonlinear partial differential equations. The question is what geometric method to use.

怎么 样 "How about the RKMK geometric integration method?"

"Using the RKMK geometric integration method to numerically solve the undamped Landau-Lifshitz equation and compare it with the analytical solution of the equation; then numerically solve the Landau-Lifshitz equation with an external magnetic field and make an error with the classic Runge-Kutta method By comparison, the problem is that although the RKMK method can better maintain the square conservation characteristics of the equation than the classic Runge-Kutta method, the RKMK geometric integration method is more difficult for the nonlinear Schrodinger equation with variable coefficients ... "

Uh ...

Various thoughts flashed through Pang Xuelin's mind ~ www.readwn.com ~ He has been thinking similarly for the past year, but he has not made any progress.

Unconsciously, Pang Xuelin stood up and walked to the window.

Through the office window, you can see that the huge solar system holographic projection is floating silently above the earth's cab.

芜 Everything in this world seems to be simple. The sun is just a dim light ball. The major planets are like fireflies, orbiting the sun along the ancient orbit.

Pang Xuelin seemed to be back on that cold night on Mars.

Under the starry sky, the various theories of Ponzi geometry that have been stagnating for a long time were quickly established in Pang Xuelin's mind. It seemed to form a wonderful connection with the system of partial differential equations, like a lightning, which illuminated the dark night sky.

Xun Pang Xuelin hit an excitement and instantly caught the fleeting inspiration.

A look of ecstasy appeared in his eyes, and he quickly turned around, picked up the red confidential phone on the table, and dialed Liu Xin: "Master, I need to retreat for a while. I have some new ideas about the problem of the orbital movement of the ground and wood. And ideas! "

Then, he opened the door to the office and the technical secretary Li Yi working outside said: "One by one, I will be closed for research during this time, don't let people disturb me, let your sister-in-law prepare food for me every day. ! "

休息室 There is a lounge in the office. In addition to eating, sleeping and bathing problems can be solved.

I didn't wait for Li Yi to respond, Pang Xuelin slammed the office door shut, a flash of excitement flashed in his eyes.

Entering the world of wandering earth for so many years, this is the first time he has such a sense of excitement in academia!