The Science Fiction World of Xueba

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

...

Early the next morning, Pang Xuelin came directly to his office, turned on the computer, and Pang Xuelin said directly: "MOSS, give me the latest simulation results of the Earth's transfer orbit today, and also provide the latest related research on the impact of the crustal movement on Jupiter's gravitational field." data!"

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

In less than a minute, various data files appeared densely on the computer desktop.

MOSS is a new generation of artificial intelligence system developed by humans on the basis of carbon-based chips. Its main body is installed in the "Pangu" supercomputer system located in the earth cab to assist the United Earth Government to control the flight orbit of the earth.

One of its clones is located on the Navigator space station and is responsible for the operation of the Navigator space station.

Pang Xuelin, as a member of the Science Committee, naturally has the authority 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 earth and wood.

...

"When the earth and wood meet, the tidal force of Jupiter will indeed greatly change the distribution of water and the atmosphere, but before the impact occurs, the atmosphere and the ocean will not leave the earth. A fluid planet, the end close to the gravitational source (near end) is gravitational Larger, the end (far end) far away from the gravitational source receives less gravitational force. This gravitational difference will elongate the fluid planet, so the gravitational force received by the near end is greater, and the gravitational force received by the far end is smaller, resulting in greater gravitational force Poor, the celestial body is stretched longer until its own gravity can no longer maintain the aggregation of the fluid, and it is pulled into pieces. This is a positive feedback process.”

"As for the earth, both the ocean and the earth are extremely thin layers. Under the action of tidal force, the atmosphere and ocean will gather at the two ends close to/far from Jupiter, and the positive feedback process will be interrupted. At this time, it is necessary to To take away the seawater and atmosphere gathered into two lumps, it is still necessary to approach the Roche limit of the rigid body (the Roche limit of the earth's rigid body where the earth and wood meet is 70,000 kilometers, which is smaller than the radius of Jupiter), and overcome the gravitational force of the entire earth."

"At a distance of 100 Jupiter radii (7 million kilometers) from Jupiter, Jupiter's gravitational pull causes tides several meters high."

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

"When the distance is 8 times the radius of Jupiter (560,000 kilometers), the atmospheric tide is enough to reduce the air pressure in most parts of the earth to a level that can cause altitude sickness. At the same time, the stress in the plate is completely released, but tends to be stable. The plate Volcanic activity continues in the intersecting areas."

"When approaching the distance between the earth and the moon (300,000 kilometers), Jupiter's tidal force reaches three-thousandths of its gravity, and part of the crustal fragmentation area at the junction of the plates becomes larger and larger."

"When Jupiter is one earth diameter (12,000 kilometers) away, Jupiter's tidal force reaches 28% of Earth's gravity, and the crust is largely broken. And the earth's tidal force is already enough to capture Jupiter's atmosphere... Perhaps it is more accurate to say it—— Jupiter’s atmosphere began to strike the earth for the first time. The earth and Jupiter’s atmosphere collided at a speed of up to 60 kilometers per second. This speed is far greater than the speed of sound, and the energy cannot escape in the form of sound waves. Jupiter’s atmosphere rushed to the earth one after another. , being continuously compressed, heated, and plasmaized."

...

"It's a bit interesting. This paper actually describes the whole process of the earth-wood impact."

Pang Xuelin forwarded this paper to the Secretary of Government Affairs after attaching his own opinions. This kind of paper has certain reference value for how the coalition government should deal with the crisis that may arise from the intersection of land and wood.

Then, he opened another file, facing the complex nonlinear partial differential equations on the computer screen,

Started to stay again.

This set of non-linear partial differential equations brings together the power of mathematicians from all over the world. The ground-wood transfer orbit equations obtained after daily corrections based on the latest supercomputing simulation results are extremely computationally intensive and can only be simulated by computers.

Theoretically speaking, it is only a Newtonian mechanics problem to calculate the safe transfer trajectory when the earth and wood meet. According to the system's equation of motion and initial conditions, the evolution of the system can be determined and the future can be predicted, which belongs to the deterministic system.

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

For example, the gravity of Jupiter caused disturbances in the crust, which caused strong earthquakes around the world, which in turn caused the planetary engines to lose thrust.

Another example is that the density inside Jupiter changes due to the gravitational force of the earth, which in turn affects the gravitational force between the two.

In addition, among the seventy-two satellites of Jupiter, four satellites have a diameter of more than 2,500 kilometers, and Callisto has a diameter of 4,800 kilometers, second only to the moon. The existence of these satellites will also have a gravitational force on the earth disturbance.

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

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

But relying on a pure mathematician's intuition, Pang Xuelin faintly felt that for the partial differential equations in front of him, the methods currently used by the mathematical community have limited accuracy.

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

"No, even if there is no way to give an analytical solution to this set of equations, a few specific exact solutions must be given!"

Pang Xuelin narrowed his eyes slightly.

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

Pang Xuelin frowned.

"Is it possible to try to use the AC=BD mode in differential geometry and Wu's differential characteristic sequence method to give solutions of various forms of equations in general form, and then give a mechanized method for finding solitary wave solutions of nonlinear partial differential equations... "

"No, although this method can convert the solution of nonlinear differential equations into the solution of nonlinear overdetermined algebraic equations, and establish a bridge between Wu's method and the solution of differential equations. However, there are uncertainties in the variables of the equations. The results are equally inaccurate!"

...

"So is it possible to use the geometric integration method to deal with this partial differential equation?"

Shiing-shen Chern, one of the greatest geometers of the 20th century, once expressed such a point of view: "The essence of physics is geometry!"

The basic formula of Newtonian mechanics F=ma, F on the left is force, which means physics, and a on the right is acceleration, which is the second derivative in mathematics, that 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 is the Ridge curvature Rik and the scalar curvature R, which is the geometry.

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

It is not uncommon to use geometric methods to solve nonlinear partial differential equations, the question is what kind of geometric methods to use.

"How about the RKMK geometric integral method?"

"The undamped Landau-Lifshitz equation was numerically solved with the RKMK geometric integration method, and compared with the analytical solution of the equation; then the Landau-Lifshitz equation with an external magnetic field was numerically solved, and the error was compared with the classical Runge-Kutta method In comparison, the problem is that although the RKMK method can better maintain the square conservation property of the equation than the classical Runge-Kutta method, the RKMK geometric integral method is more difficult for the nonlinear Schrodinger equation with variable coefficients..."

...

Various ideas flashed in Pang Xuelin's mind. For the past year, he had been thinking about something similar, but he hadn't made any progress.

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

Through the window of the office, one can see that the huge holographic projection of the solar system is silently suspended above the earth cab.

All the chaos in this world seems to be simplified. The sun is just a dim ball of light, and the planets are like fireflies, orbiting the sun along the eternal orbit.

Pang Xuelin seemed to have returned to that cold night on Mars.

Under the starry sky, various theories of Ponzi geometry, which had been stagnant for a long time, were quickly established in Pang Xuelin's mind, and they seemed to form a wonderful connection with the partial differential equations, like a lightning bolt, illuminating the dark night sky.

Pang Xuelin shuddered, and instantly grasped the fleeting inspiration.

There was a hint of ecstasy in his eyes, he turned around quickly, picked up the red confidential phone on the table, and dialed Liu Xin: "Master, I need to retreat for a while, and I have some new ideas about the issue of the earth-wood transfer track." and ideas!"

Then, he opened the door of the office again, and Li Yiyi, the technical secretary working outside, said, "Yiyi, I'm going to retreat for research during this time, don't let people disturb me, just ask your sister-in-law to prepare food for me every day." !"

There is a rest room in the office, in addition to eating, sleeping and bathing problems can be solved.

Without waiting for Li Yiyi to react, Pang Xuelin slammed the office door shut, a hint of excitement flashed in his eyes.

After entering the world of Wandering Earth for so many years, this is the first time he has such a sense of eagerness academically!