Biological Motion

Abstract

In many sciences, including biology, we need to model motion that has some random element to it. In physics, for example, we might be concerned with molecular diffusion, the random motion of molecules in a fluid. In addition to undergoing diffusion, molecules within a fluid may also be carried along by a current in the fluid, a process known as advection. A microscopic theory of random motion is a description of the statistical properties of this motion for a molecule or an ensemble of molecules, a problem investigated by Einstein. We might also hope to gain from a consideration of these properties an idea of how the bulk properties of the fluid, such as its pressure, temperature, density and velocity field, vary with space and time. This is a macroscopic theory of random motion, which may be derived using a random walk approach or a continuum approach. In this book we shall restrict ourselves to a continuum approach, although this precludes us from deriving detailed models of individual-based behaviour and stochastic effects. There is some material on the website about the alternatives.