Notes
Preliminary Study
Here are some small-scale research projects I've completed. During these projects, I observed some intriguing phenomena that I think warrant further exploration in the future.
Extended SIR Models with Monte Carlo Simulations
To enhance the completeness of the SIS model, additional variables can be included,
such as in the SEIR model, which introduces an "exposed" variable (E). However, adding more variables increases the model's complexity,
making the differential equations more challenging to solve. To manage this complexity, we use the Monte Carlo method to simulate
the equations. This approach simplifies the simulation of multiple differential equations and provides clear results.
Neural Network and the Renormalization Group
The renormalization group theory is an influential tool used to study phase transitions,
providing deep insights into how systems behave at different scales. On the other hand,
neural networks represent a sophisticated theoretical framework within artificial intelligence,
designed to model and understand complex patterns and relationships in data.
Recent developments have highlighted an intriguing connection between these two areas:
neural networks can be interpreted as a form of renormalization process.
This perspective suggests that the mechanisms underlying neural networks bear a resemblance to the principles of renormalization,
where the process of simplifying and scaling data in neural networks parallels the renormalization techniques
used in phase transition analysis. To explore this connection further, we analyze and discuss various numerical
results that illustrate the similarities between neural networks and renormalization processes.
This examination sheds light on how concepts from one domain can enrich our understanding of the other.
Numerical Simulation of Simplify Stellar Wind Model
The magnetohydrodynamics (MHD) equation model is considered one of the most straightforward frameworks for describing
the behavior of plasma, combining the principles of magnetism and fluid dynamics. Although this model offers a foundational
understanding, the complex nature of plasma introduces significant challenges that extend beyond the capabilities of the
MHD equations alone. To address these challenges and gain deeper insights into plasma behavior, we construct a
detailed stellar wind model. By examining this model, we can observe and analyze a range of phenomena related to plasma dynamics.
This approach allows us to investigate and better understand some of the more intriguing and complex behaviors exhibited by plasma,
offering valuable perspectives on its properties and interactions in various contexts.
Rare Events and Phase transition in One-Dimensional Lattice Prey-Predator Model
