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Parameter Spaces
Physicists are known for order-of-magnitude calculations on the backs of envelopes. What are the relevant length, time, and energy scales? What dimensionless parameters can be formed? Toy models can provide valuable intuition; real models should be just complex enough to capture the phenomenon of interest. Einstein, with all his brainpower, was deeply impressed by classical thermodynamics — by its simplicity and its wide range of applicability.
Physics has numerous areas of overlap with the other sciences and engineering. Starting in the 20th century, some physicists became interested in biology. Erwin Schrödinger, one of the fathers of quantum theory, wrote What Is Life? in 1944. Certainly, he reasoned, the laws of physics and chemistry must apply within living things — what basic biological questions can we ask, e.g., in terms of information content and entropy increase? Physicists following in Schrödinger's footsteps would form part of the quantitative biology community, applying their training to study problems as diverse as neuron firing, motor proteins, and cancer progression.
What can physics tell us about the aqueous environment in/around a micron-sized cell? The Reynolds number fluid parameter $$\mathrm{Re} \ll 1$$, so inertia is unimportant — there is no drifting! Water and dissolved ions screen out all electrostatic interactions beyond the nanometer-sized Debye length. While living systems are, by definition, out-of-equilibrium, local equilibria often exist. In general, diffusive and dissipative forces dominate, so the most effective tools are those of statistical mechanics and stochastic processes.
In contrast to a living cell, a pure, crystalline solid is a very different lump of condensed matter, indeed. The solid has the well defined order and symmetry of the unit cell extending in all directions. While its ions do experience vibrations, they can generally be treated as a fixed lattice through which the valence electrons flow. On the other hand, the cell consists of heterogeneous fluid contents encapsulated by a cell membrane. Despite its hodgepodge character, the cell does contain many components that are highly ordered and even capable of self-organizing.
In modeling some aspect of cell behavior, model parameter values must typically come from experimental data. For the solid, however, properties can be calculated from first principles. Given elemental composition and unit cell structure, density functional theory can solve the equations of quantum mechanics to yield electronic structure. Transport theory can then be used to calculate bulk properties useful to the MSE community — how well does this material conduct heat and electricity?
© 2011-2019 Ted Malliaris