where σ is the stress tensor, ǫ = 12 (∇u +∇u) T is the strain tensor, f is a body force per unit mass (gravity is a typical example), qT is a volume source (it may model chemical reactions, Joule effects, radioactive decay, etc.), and jT is the heat flux. In addition to the above three fundamental conservation equations, one may also have to add L equations that accounts for the conservation of...

When anticommuting Grassmann variables are introduced into a fluid dynamical model with irrotational velocity and no vorticity, the velocity acquires a nonvanishing curl and the resultant vorticity is described by Gaussian potentials formed from the Grassmann variables. Upon adding a further specific interaction with the Grassmann degrees of freedom, the model becomes supersymmetric.

Extreme sports such as canyoneering have expanded greatly since the turn of the century yet little scientific attention has been paid to the analyses of the dangers of those activities. The author was much involved in promoting one such sport, namely canyoneering, and presents this paper as an example of the kind of fluids engineering analyses that are needed in order to objectively quantify th...

Interest groups sometimes seek to attract broad public attention to their issues as a means to influence public policy decisions by political actors. How can business firms compete against this strategy? The purpose of this paper is to develop a theoretical framework to analyze the potential impact of nonmarket strategies on the formation of public opinion. To do so, we use recent developments ...

where x = φ(X, T ) is the position of the material point X at time T . We will refer to X as a material, or Lagrangian point, and x as a spatial or Eulerian point. If Ω ⊂ B is a material region, we denote by ΩT = φ (Ω, T ) the spatial region occupied by the material points in Ω at time T . We assume that the deformation φ is smooth, with a smooth inverse X = Φ(x, t). Here, we write T = t for th...

We studied splashing on both smooth and rough dry surfaces using high speed photography. For smooth substrates, a striking phenomenon is observed: splashing can be completely suppressed by decreasing the pressure of the surrounding gas. The threshold pressure where a splash first occurs is measured as a function of the impact velocity and found to depend on the molecular weight of the gas and t...

(i) A study of the fluids in simple flow situations, such as those found in Rheometry. (ii) The construction of suitable constitutive equations for the non-Newtonian fluids under test. (iii) The use of these constitutive equations in the prediction of behavior in complex flows of practical importance. (iv) An experimental study of the behavior of non-Newtonian fluids in the complexflow situatio...