Within the framework of a simple Rouse-type model we present exact analytical results for dynamical critical behaviour on the sol side of the gelation transition. The stress-relaxation function is shown to exhibit a stretched-exponential longtime decay. The divergence of the static shear viscosity is governed by the critical exponent k = φ − β, where φ is the (first) crossover exponent of rando...

Wire-coating flow is simulated, involving polymer melt coatings and tube-tooling process design. A finite element method is employed, based on a semi-implicit time-stepping Taylor-Galerkin/pressure-correction scheme. The exponential Phan-Thien/Tanner model is used in its multi-mode form to represent a high-density polyethelyne (HDPE) polymer. Both shear-thinning and elongation-softening propert...

Non-Gaussian velocity distribution in star forming region is reproduced by inelastic clump collision model. We numerically calculated the evolution of inelastic hard spheres in sheared flow, which corresponds to cloud clumps in differential galactic rotation. This system fluctuates largely around equilibrium state, creating clusters with inelastic collisions and destroying them with shear motio...

We study the inviscid damping of Couette flow with an exponentially stratified density. The optimal decay rates of the velocity field and the density are obtained for general perturbations with minimal regularity. For Boussinesq approximation model, the decay rates we get are consistent with the previous results in the literature. We also study the decay rates for the full Euler equations of st...

The shear instability mechanism for generation of surface water waves (Miles 1957) is re-examined in light of the nonnormality of the underlying linear operator. The associated eigenproblem and adjoint eigenproblem are solved numerically and a clarification to previous perturbation solutions of the eigenproblem discussed. The optimal excitation problem is solved in the asymptotic limit t → ∞ an...

Corrections to elastic moduli, including the effective shear modulus, of a solid neutron star crust due to electron screening are calculated. At any given mass density the crust is modelled as a body-centered cubic Coulomb crystal of fully ionized atomic nuclei of a single type with a polarizable charge-compensating electron background. Motion of the nuclei is neglected. The electron polarizati...

We report on the formation of surface instabilities in a layer of thermoreversible ferrogel when exposed to a vertical magnetic field. Both static and time dependent magnetic fields are employed. Under variations of temperature, the viscoelastic properties of our soft magnetic matter can be tuned. Stress relaxation experiments unveil a stretched exponential scaling of the shear modulus, with an...

We consider a reaction-diffusion system of the KPP type in a shear flow and with a non-zero heat loss parameter. We establish criteria for the flame blow-off and propagation, and identify the propagation speed in terms of the exponential decay of the initial data. We prove existence of traveling fronts for all speeds c > max(0, c∗) in the case Le = 1, where c∗ ∈ R. That seems to be one of the f...

Channel flow of an incompressible fluid at Reynolds numbers above 2400 possesses a number of different spatially localized solutions that approach laminar flow far upstream and downstream. We use one such relative time-periodic solution, which corresponds to a spatially localized version of a Tollmien-Schlichting wave, to illustrate how the upstream and downstream asymptotics can be computed an...

We prove that genuine nonuniformly hyperbolic dynamics emerge when flows in RN with homoclinic loops or heteroclinic cycles are subjected to certain time-periodic forcing. In particular, we establish the emergence of strange attractors and SRB measures with strong statistical properties (central limit theorem, exponential decay of correlations, et cetera). We identify and study the mechanism re...