In classical physics it is a simple fact that if you knew enough information nothing could be beyond prediction. If quantum physics was to be ignored someone could have calculated the entire universe provided they knew every detail of the big bang. When companies make predictions they are not of this kind. You will probably heard the practically vapid phrase that “correlation does not equal causation” but the simple fact is that correlation is the only thing required. If 90% of people who buy pens online also buy paper later, who cares if its causation. Advertisements will appear for various notepads because it is statically likely the pen buyer will soon be looking for one. In a similar way it is estimated that some life insurance companies have so much information that they can predict the date of someone’s death (based on neighbourhood, average income, previous family medical records, ect) to within a year.
When a system’s particles interact under a repulsive inverse power law, it means that particles will repel each other and the force with which one particle experiences from another can be stated generally as:
F = k / rn
where F is the force exerted on the particle, k is a constant, r is the distance between the two two particles and n is the order of the interaction.
Svante Arrhenius was a Swedish physicist and chemist whose name should be recognisable to anyone who has studied physical chemistry due to his ever relevant Arrhenius equation which describes how a value called the rate constant changes with activation energy and temperature. Apart from physical chemistry he worked on geology and the origin of the ice ages. As part of this study, in 1896, he wrote a paper in which he calculated that the effect of halving the carbon dioxide in the atmosphere would decrease the temperature of Europe by about 4 °C. This was the first prediction linking carbon dioxide to temperature changes ever made and still provides solid evidence for the premise.
Animals in nature have an uncanny ability to operate as a single unit with collective movement when they group together. Flocks of birds have been found to fit statistical models, people walking together naturally match each others step, bacteria can form groups that then move as one, with each individual responding to the same chemical stimuli.
Back in 1855 a mathematical physicist turned doctor, called Adolf Eugen Fick, created what is now known as Fick’s laws of diffusion. The first is simply that the the diffusive flux is proportional to the concentration gradient and the second is that the rate of concentration change is proportional to the derivative of the concentration gradient. Later the same conclusion was reached when applying the method of random walks to particles in suspension and the final result was reached where the mean squared displacement of a particle is proportional to the time since it stared to move. This is considered the standard description of the diffusion process:
〈 χ2 〉 ∝ t
In chemistry Hund’s rule is one that may not always be remembered associated with his name, but is nonetheless always recalled. It is the fact that electrons will always attempt to avoid pairing with another electron in an orbital and so all orbitals in a shell will gain one electron before they start doubling up. This can be simply explained as this arrangement allows the electrons to exist nearer the nucleus and so makes the overall atom more stable.
Quite a while ago I wrote a post on materials that are called auxetic. This is where the Poisson ratio, the ratio of how much thinner a material gets when stretched a certain amount, is negative. This means that if you had a rod of auxetic material and you tried stretching it at the ends, it would get thicker in the middle. To the same degree compressing actually makes it get thinner, the opposite of most materials we encounter in every day life. The actual production of auxetic materials, a type of mechanical metamaterial, is actually quite easy with multiple methods being suggested such as moulding, 3D printing and the use of precise incisions into certain regular materials.