Dynamics of Hyperbolically Symmetric Fluids

Traveling Waves of Some Symmetric Planar Flows of Non-Newtonian Fluids

We present some variants of Burgers-type equations for incompressible and isothermal planar flow of viscous non-Newtonian fluids based on the Cross, the Carreau and the power-law rheology models, and on a symmetry assumption on the flow. We numerically solve the associated traveling wave equations by using industrial data and in order to validate the models we prove existence and uniqueness of ...

Fluid Dynamics Without Fluids

Fluid dynamics of dilatant fluids.

A dense mixture of granules and liquid often shows a severe shear thickening and is called a dilatant fluid. We construct a fluid dynamics model for the dilatant fluid by introducing a phenomenological state variable for a local state of dispersed particles. With simple assumptions for an equation of the state variable, we demonstrate that the model can describe basic features of the dilatant f...

Experimental nonlinear dynamics of fluids

On *m Nearly six decades ago, Stoker, in the introduction to his seminal book on nonlinear vibrations (Stoker 1950), pointed out ‘It is perhaps worth while to consider for a moment the reasons why one should be interested particularly in the nonlinear problems in mechanics. Basically the reason is, of course, that all of the problems in mechanics are nonlinear from the outset, and the lineariza...

Hyperbolically Discounted Temporal Difference Learning

Hyperbolic discounting of future outcomes is widely observed to underlie choice behavior in animals. Additionally, recent studies (Kobayashi & Schultz, 2008) have reported that hyperbolic discounting is observed even in neural systems underlying choice. However, the most prevalent models of temporal discounting, such as temporal difference learning, assume that future outcomes are discounted ex...