# Materials Modeling

### Lecture 1: Introduction to Material Science

![Ashby Chart sourced from ntopology](https://354051965-files.gitbook.io/~/files/v0/b/gitbook-x-prod.appspot.com/o/spaces%2F-M7czuNAEqLJsrfUWARA%2Fuploads%2FsLxVMimVfaFWHt1CPl2f%2FFigure-1-1024x791.png?alt=media\&token=075e07b2-8fa4-4a42-89f6-2a0df07d9a7a)

Multiscale Modeling is touched on in Fluid Mechanics but here, will traverse the scale through the lectures. 

Ab Inito Methods derive materials properties from first principals or wave equation 

* Pros
  * electronic and structural behavior and properties 
  * bond breaking and formation in chemical reaction
  * can systematically improve results to prove quality
  * in principal, can obtain exact properties
* Cons

  * very small systems, \~O(10E2) atoms
  * very small timescales, \~O(10E-12) or pico seconds
  * numerically expensive on even super computers of \~O(10E15) flops

Atomistic Methods is the range of semi classical statistical mechanics for thermodynamic and transport properties

* Pros
  * Systems larger on scale of \~O(10E4) and \~O(10E6) atoms
  * Larger timescales of \~O(10E-9) to O(10E-6) second 

     
* Cons
  * results depend on force field used 
  * Transport properties dependent on macroscale conditions which affect physical processes

Mesoscale methods is a level of simplification treating clusters of atoms as blobs of matter. An abstraction which allows for some computational savings by calculation as entities moving through a potential field. 

* Pros
  * Study structural features of complex systems on size \~O(10E8) or more
  * Dynamic processes on the order of a second
* Cons
  * Mostly only qualitative tendencies, with quality difficult to ascertain
  * Approximations limit insight 

Continuum Methods: assume matter can be treated as field quantity which changes continuously. Solve balance equations, per FEM and CFD.

* Pro:  rest of the time lengthscale diagram is accessible 
* Con Require viscosity, diffusion coefficients, and other transport properties

Upscaling is the using a lower lengthscale information to inform the properties of higher length scales in a deductive approach

Downscaling is using higher scale, often experimental information, to inform lower order parameters. More difficult due to non-uniqueness.

### Lecture 2: Ab Inito Principals, Fundamentals

### Lecture 3: Ab Inito and Density Functional Theory, Part 1

### Lecture 4: Ab Inito and DFT, Part 2

### Lecture 5: Linux

### Lecture 6: Ab Inito and DFT, Part 3

### Lecture 7: Molecular Dynamics (MD), Introduction

### Lecture 8: MD Introduction to Integrators

### Lecture 9: MD Force Fields and Ensembles

### Lecture 10: MD Static Properties

### Lecture 11: MD Dynamic Properties

### Lecture 12: MD Tricks of the Trade

### Lecture 13: Project Guidelines 

### Lecture 14: Introduction to Monte Carlo Methods

### Lecture 15: Ising Model

### Lecture 16: Kinetic and Reverse Monte Carlo

### Lecture 17: Brownian Dynamics

### Lecture 18: Dissipative Particle Dynamics

### Lecture 19: Continuum Methods and Beyond