## Computational Neuroscience

Computational neuroscience: neuron and network simulation

# Neuron

The neuron is the most common component in our brain,  we have nearly 86 billion neurons and 1000 trillion synaptic connections, estimates to a computer with a 1 trillion bit per seconds processor # Computational Neuroscience

Is the field of study in which we measure and simulate the neurons process. Our brain is a complex machine and its behavior is non-linear.

We need previous knowledge of electronics, ODE’s, neurobiology, chemistry, and programming.

## Dynamic Systems

N-Order Linear Systems

I have done a project for my math class where we analyze the linear systems. We have classified the first and second-order linear systems and give a general formula for an n-linear system. We have used algebra notation and we have encountered with the companion matrix power to the n problem.

The n-linear systems are used widely in finance for loans, interests, etc.

GitHub repository: DynamicSystem

## Computational Fluid Dynamics (CFD)

Navier-Stokes + Incompressible + Finite difference method

Discretization methods for approximating the Partial Differential Equations (PDEs):

1. Finite Difference (FD) 2. Finite Elements (FE)
3. Finite Volume (FV)

#### Finite Difference (FD) Taylor’s polynomial   ## Spacecraft Trajectory Optimization

Trajectory optimization using AI

Spacecraft mission will become more common. There are relevant open projects such that Mars colonization and exploring missions outside the Solar System.

These missions require high accuracy calculations because the error propagates in time and would be able to modify the trajectory.

There are many ways to face this problem: analytical or numerical approaches.

The analytical approaches could only be used for simplified problems, and thus it is really restrictive.

The numerical approaches commonly used and include metaheuristics and nonlinear programming. I have used genetic algorithms to solve a basic problem which consists of optimizing trajectory to travel to Mars from the Earth.

## Nuclear Fusion + AI

Fusion Reactor Simulations + Deep learning

Fusion power is a proposed form of power generation that would generate electricity by using heat from nuclear fusion reactions.

There are many methods to achieve the fusion: magnetic confinement, inertial confinement, electric pinches, inertial electrostatic confinement, …

#### magnetic confinement – tokamak

Pulsotron is a Tokamak fusion power reactor. It is an evolutionary prototype that was designed by Javier Luis López. The simulations were made using C++ and OpenGL.