Lecture

Monte Carlo methods: single particle diffusion

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Description

This lecture introduces Monte Carlo methods for simulating single particle diffusion in cementitious materials, focusing on the use of random numbers in simulation, random functions, and random number generators. It covers a simple hopping model on a lattice, Monte Carlo time, and the self-diffusion coefficient. The lecture also discusses diffusion from a line at a specific position, providing insights into the dynamics of water and ions in cement microstructures.

In MOOC

Sorption and transport in cementitious materials

In the MOOC: “Cement chemistry and sustainable cementitious materials”; you learned how to create more sustainable cementitious materials. But concrete is not an inert rock. It is a dynamic porous material, which can exchange water, gas and ions with its environment. Through physical and chemical interactions, these exchanges can have dramatic consequences: cracks due to shrinkage, reinforcement bars corrosion, spalling, … For a true sustainability, the durability of cementitious materials should not be f

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Related concepts (32)

Random number generation

Random number generation is a process by which, often by means of a random number generator (RNG), a sequence of numbers or symbols that cannot be reasonably predicted better than by random chance is generated. This means that the particular outcome sequence will contain some patterns detectable in hindsight but unpredictable to foresight. True random number generators can be hardware random-number generators (HRNGs), wherein each generation is a function of the current value of a physical environment's attribute that is constantly changing in a manner that is practically impossible to model.

Hardware random number generator

In computing, a hardware random number generator (HRNG), true random number generator (TRNG) or non-deterministic random bit generator (NRBG) is a device that generates random numbers from a physical process capable of producing entropy (in other words, the device always has access to a physical entropy source), rather than by means of an algorithm. Such devices are often based on microscopic phenomena that generate low-level, statistically random "noise" signals, such as thermal noise, the photoelectric effect, involving a beam splitter, and other quantum phenomena.

Diffusion

Diffusion is the net movement of anything (for example, atoms, ions, molecules, energy) generally from a region of higher concentration to a region of lower concentration. Diffusion is driven by a gradient in Gibbs free energy or chemical potential. It is possible to diffuse "uphill" from a region of lower concentration to a region of higher concentration, like in spinodal decomposition. Diffusion is a stochastic process due to the inherent randomness of the diffusing entity and can be used to model many real-life stochastic scenarios.

Molecular diffusion

Molecular diffusion, often simply called diffusion, is the thermal motion of all (liquid or gas) particles at temperatures above absolute zero. The rate of this movement is a function of temperature, viscosity of the fluid and the size (mass) of the particles. Diffusion explains the net flux of molecules from a region of higher concentration to one of lower concentration. Once the concentrations are equal the molecules continue to move, but since there is no concentration gradient the process of molecular diffusion has ceased and is instead governed by the process of self-diffusion, originating from the random motion of the molecules.

Pseudorandom number generator

A pseudorandom number generator (PRNG), also known as a deterministic random bit generator (DRBG), is an algorithm for generating a sequence of numbers whose properties approximate the properties of sequences of random numbers. The PRNG-generated sequence is not truly random, because it is completely determined by an initial value, called the PRNG's seed (which may include truly random values).

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