Why do we need to look at things at a microscopic level?

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Molecular dynamics (MD) simulation is a computational method for studying the physical movements of atoms and molecules. It involves using computer algorithms to integrate the equations of motion for a system of interacting particles, in order to predict the evolution of the system over time.

In an MD simulation, the positions, velocities, and forces on each particle are calculated at discrete time steps, typically on the order of femtoseconds (10^-15 seconds). The simulation starts with an initial configuration of the system, which may be taken from experimental measurements or generated using theoretical models. The forces acting on the particles at each time step are calculated based on the potential energy of the system, which is determined by the interactions between the particles. These forces are used to update the positions and velocities of the particles, and the process is repeated until the simulation reaches the desired length of time.

MD simulations can be used to study a wide range of systems, including gases, liquids, solids, and biomolecules. They are a valuable tool for understanding the behavior of complex systems at the atomic level, and have many applications in areas such as materials science, chemistry, and biology.

What is NPT ensemble?

NPT is a type of simulated system in which the number of particles, the pressure and the temperature are held constant.

Here the “constant” is not saying that everything will not be changed, but an average.

When we talk about the average, the time duration must be considered. However, how long an NPT simulation cannot be pre-determined. I guess it needs to flow the following principles:

1. Simulate without divergence
2. Does the result make sense based on the primary parmeter?
3. Increase and decrease the time duration, how the amount of the result will be changed?

What is the relation between the microscopic and macroscopic parameters?

To understand the parameters at the macroscopic level, it is often necessary to change the perspective from macroscopic to microscopic. At the microscopic level, there are several parameters to consider, such as:

• The positions and velocities of the individual particles in the system
• The masses of the particles
• The charges of the particles (if they are charged)
• The strength of the interactions between the particles (such as the strength of the gravitational or electromagnetic forces)
• The shape and size of the particles
• The temperature of the system (which determines the average kinetic energy of the particles)
• The density of the system (which determines the number of particles in a given volume)

By studying the relationship between these parameters at the microscopic level, it is possible to make predictions at the macroscopic level, which are more useful for practical applications. This is where statistical mechanics comes in, as it helps us understand the behavior of large systems by considering the behavior of their individual components in phase space.

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What is phase space in classical statistical mechanics?

Two groups of vectors: location vector \[\mathbf{r}_1(t), \ldots, \mathbf{r}_N(t) \] and momentum vector \[ \mathbf{p}_1(t), \ldots, \mathbf{p}_N(t) \].

This 6N-dimensinal (2dN in d dimension) space is called phase space.

What is microcanonical ensemble?

The microcanonical ensemble is composed of a collection of systems isolated from any surroundings (Tuckerman 2010).

Basic concepts

• What is temperature? It is a measure of the average kinetic energy of the particles in a substance.
• What is absolute pressure? It’s a measure of pressure against the pressure in a vacuum.
• What is Gauge pressure? It’s a measure of the pressure difference between the atmosphere and the absolute pressure.

Stuip question

Why computational fluid dynamics can predict a large number of particles with high accuracy?

We all know that it is impossible to obtain an exact solution for the three-body problem. If we consider small particles instead of celestial objects, the problem will be more difficult because more forces are needed for consideration. But in computational fluid dynamics, we can obtain relatively good predictions even compare to experimental studies. Remember, in CFD, there are significant much more particles involved. So, what is the reason of this mismatch?

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