Dispersion and deposition of aerosol particles over two square cylinders confined in a channel in laminar unsteady vortical flow were investigated numerically. Lattice Boltzmann method was used to calculate fluid characteristics and modify Euler method was employed as Lagrangian particle tracing procedure to obtain particle trajectories. Drag, Saffman lift, gravity, buoyancy and Brownian motion...

A radiative transfer equation is used to model the diffuse multiple scattering of ultrasound in a medium containing discrete random scatterers. An assumption of uncorrelated phases allows one to write an equation of energy balance for the diffuse intensity. This ultrasonic radiative transfer equation contains single-scattering and propagation parameters that are calculated using the elastic wav...

A relativistic Navier-Stokes equation is constructed as the equation of motion of a gauge-invariant bosonic lagrangian. It is shown that the quantum-electrodynamic-like lagrangian is suitable for this purpose with a particular form of gauge field, A µ = φ, A ≡ −c 2 1 − | v| 2 /c 2 , − v. The equation of motion coincides with the classical Navier-Stokes equation at non-relativistic limit | v| ≪ c.

We investigate the experimental limits of validity of the Stokes–Einstein equation. There is an important difference between diffusion and self-diffusion. The experimental evidences show, that in the case of selfdiffusion the product Dg/T is constant and the Stokes–Einstein equation is still valid. On the other hand, comparison of existing experimental data, on viscosity g and diffusion coeffic...

A relativistic Navier-Stokes equation is constructed as the equation of motion of a gauge-invariant bosonic lagrangian. It is shown that the quantum-electrodynamic-like lagrangian is suitable for this purpose with a particular form of gauge field, A µ = φ, A ≡ −c 2 1 − | v| 2 /c 2 , − v. The equation of motion coincides with the classical Navier-Stokes equation at non-relativistic limit | v| ≪ c.

We consider an equation similar to the Navier-Stokes equation. We show that there is initial data that exists in every Triebel-Lizorkin or Besov space (and hence in every Lebesgue and Sobolev space), such that after a finite time, the solution is in no Triebel-Lizorkin or Besov space (and hence in no Lebesgue or Sobolev space). The purpose is to show the limitations of the so called semigroup m...

In this paper, we derive a posteriori error estimates for space-discrete approximations of the timedependent Stokes equations. By using an appropriate Stokes reconstruction operator, we are able to write an auxiliary error equation, in pointwise form, that satisfies the exact divergence-free condition. Thus, standard energy estimates from partial differential equation theory can be applied dire...

In this article, a non linear family of spaces, based on the energy dissipation, is introduced. This family bridges an energy space (containing weak solutions to Navier-Stokes equation) to a critical space (invariant through the canonical scaling of the Navier-Stokes equation). This family is used to get uniform estimates on higher derivatives to solutions to the 3D Navier-Stokes equations. Tho...

This is the second of two papers on the zero-viscosity limit for the incompressible Navier-Stokes equations in a half-space in either 2D or 3D. Under the assumption of analytic initial data, we construct solutions of Navier-Stokes for a short time which is independent of the viscosity. The Navier-Stokes solution is constructed through a composite asymptotic expansion involving the solutions of ...