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...

We discuss well-posedness and convergence theory for the DPG method applied to a general system of linear Partial Differential Equations (PDEs) and specialize the results to the classical Stokes problem. The Stokes problem is an iconic troublemaker for standard Bubnov Galerkin methods; if discretizations are not carefully designed, they may exhibit non-convergence or locking. By contrast, DPG d...

The quantum theory of forward Stokes generation by means of stimulated Raman scattering is extended to the case of a colored (finite-bandwidth) chaotic pump, which has both amplitude and phase fluctuations. In both transient and steady-state limits the mean Stokes intensity is found to be enhanced over that resulting from a coherent pump. In the limit that the chaotic-pump bandwidth becomes lar...

In this article, we study the steady generalized Navier-Stokes equations in a half-space in the setting of variable exponent spaces. We first establish variable exponent spaces of Clifford-valued functions in a half-space. Then, using this operator theory together with the contraction mapping principle, we obtain the existence and uniqueness of solutions to the stationary Navier-Stokes equation...

A generalization of criticality – called secondary criticality – is introduced and applied to finite-amplitude Stokes waves. The theory shows that secondary criticality signals a bifurcation to a class of steady dark solitary waves which are biasymptotic to a Stokes wave with a phase jump in between, and synchronized with the Stokes wave. We find the that the bifurcation to these new solitary w...

The spin rate Omega of neutron stars at a given temperature T is constrained by the interplay between gravitational-radiation instabilities and viscous damping. Navier-Stokes theory has been used to calculate the viscous damping time scales and produce a stability curve for r modes in the (Omega,T) plane. In Navier-Stokes theory, viscosity is independent of vorticity, but kinetic theory predict...

675 Theory of spatially periodic progressive (propagat ing with constant velocity without change of the amplitude) waves in two dimensional (2D) potential flow of an ideal incompressible fluid with free surface in gravitational field was founded in pioneering works by Stokes [1, 2] and developed further by Michell [3], Nekrasov [4, 5], and many others (see, e.g., book [6] by Sretenskii for revi...

In this paper, the nonlinear dynamic buckling of double-walled boron-nitride nanotube (DWBNNT) conveying viscous fluid is investigated based on Eringen's theory. BNNT is modeled as an Euler-Bernoulli beam and is subjected to combine mechanical, electrical and thermal loading. The effect of viscosity on fluid-BNNT interaction is considered based on Navier-Stokes relation. The van der Waals (vdW)...