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Undergraduate courses - University of Aberdeen
Undergraduate courses - University of Aberdeen
Statistical Physics (also known as Statistical Mechanics), together with Quantum Mechanics and Relativity theory, form the cornerstone in our modern understanding of the physical world. Statistical Physics derives the phenomenological laws of Thermodynamics from fundamental principles and the probabilistic treatment of the underlying microscopic system.
This course starts by a brief recap of Thermodynamics and an introduction to Probability theory, which set up the background needed to understand the foundations of Statistical Physics. Then, the microcanonical and canonical ensembles are discussed in detail, which allow to explain how thermodynamical irreversibility (sometimes referred as the arrow of time) emerges naturally from reversible microscopic dynamics. After, quantum statistics (i.e., Bose-Einstein and Fermi-Dirac statistics) are discussed and applied. These applications are limited to non-interacting (or quasi non-interacting) systems, which include computing the specific heats of solids and of monoatomic and simple diatomic gases, explaining blackbody radiation, and solving the Ising model in the mean-field approximation to explain para- and ferro-magnetism. Finally, this course introduces Stochastic Processes, focusing on Brownian motion and random walks. This allows to introduce the Langevin and Fokker-Planck equations for stochastic systems, offering a simple context in which the central limit theorem can be introduced.
This course consists of two courses which were merged several years ago, so it maintains a structure of two halves. The two are: Solids, Liquids, and Gases, and Thermodynamics. Overall, the current PX3014 course aims to show how the properties of energy and matter can be explained by simple physical principles.
The first part covers the physical properties of (the main) three types of matter: gases, liquids, and solids. Namely, it explores the mechanical properties, going over the kinetic theory of gases, fluid hydrostatics, elasticity of solids, fluid dynamics, and viscoelasticity. The second part of the course explores the thermodynamic behaviour of these matter phases to try to understand how and why energy – particularly heat – flows in matter, introducing the concept of entropy. Building on this foundation, the laws of thermodynamics are explained, and the following topics are covered: heat capacity and engines, thermodynamic potentials, Maxwell relations, properties of ideal gases, and phase transitions.
This course is an introduction to physical phenomena that depend on time, with emphasis on oscillatory and wavelike behaviour. It will focus on studying the dynamical aspect of these phenomena, which means dealing with the rules that govern the evolution of the system (such as Newton’s second law of motion). Because of this dynamical aspect, the concept of a first- and second-order differential equations will be used to unify the treatment of mechanical and electrical phenomena. This will allow to introduce the mathematical framework for simple harmonic oscillations, damped harmonic oscillations, and forced harmonic oscillations, which lead to resonant behaviour. Wave motion will be used to introduce the ideas behind Fourier transforms and partial differential equations. The course also has a section on scientific programming, where the students learn how to use MATLAB programming language to numerically solve differential equations.
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