The free-surface effect
A simulation of the free-surface effect, which can lead to a ship carrying a liquid cargo to capsize where the same ship carrying the same mass of solid cargo will float upright.
Physics
59 posts on physics. All posts · RSS feed
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Higher Orders of Rainbow
The different orders of rainbow caused by different number of internal reflections of light in a rain droplet are simulated and a derivation of their angular size given. The provided code simulates the rainbow orders that would be observed away from and towards the sun, …
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Modelling a Phase Change with Kawasaki Dynamics
The Kawasaki dynamics formalism from statistical physics provides a simple model of a phase change (for example, the condensation of a gas at low enough temperature). Considering a gas of particles on a two-dimensional lattice of cells, a given configuration's energy can be calculated as …
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Which is the most intense line in a rotational spectrum?
Abstract Most textbooks and lecture notes on molecular spectroscopy assert that the most intense transition in the pure rotational (microwave) absorption spectrum () of a closed-shell, diatomic molecule is given, as a function of temperature, by the formula (where is the molecule's rotational constant and …
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Transforming the molecular kinetic energy operator to an origin at the centre of mass of the nuclei
This previous article derived the form of the kinetic energy operator for a diatomic molecule with the space-fixed origin at the molecular centre of mass: where is the reduced mass of the nuclei, is the electron mass, is the total molecular mass (including the electrons), …
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Transforming the molecular kinetic energy operator to an origin at the molecular centre of mass
The molecular kinetic energy operator for a diatomic molecule may be written where and are the momentum operators for the two nuclei and electrons, respectively. are the masses of the nuclei and is the electron mass. The vector differential operator del is and being the …
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The Kapitza pendulum
The Kapitza pendulum is an inverted pendulum that can balance stably when driven by an oscillating vertical displacement. Its behaviour can be described using Lagrangian mechanics and modelled in Python, using the NumPy, SciPy and Matplotlib libraries.
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The Kelvin wake pattern
An object (ship, duck, etc.) travelling across the surface of water at a constant velocity $\boldsymbol{u}$ produces a characteristic wake pattern of waves first described by Lord Kelvin. In his model of the effect, he assumed deep, still water, neglected surface tension, and restricted the …
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The two-dimensional wave equation
The wave equation is a second-order linear partial differential equation describing the behaviour of mechanical waves; its two (spatial) dimensional form can be used to describe waves on a surface of water: $$ \frac{\partial^2 u}{\partial t^2} - c^2\left( \frac{\partial^2 u}{\partial x^2} + \frac{\partial^2 u}{\partial y^2} …
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Fitting the heat capacity curve of a diatomic molecule
The molar constant-pressure heat capacity, of many diatomic molecules above room temperature shows an increase from roughly to around and then higher as temperature increases. For example the graph below plots as a function of for the molecules , , , .
