Related papers: Wave hierarchies in viscoelasticity
Unstable equilibrium solutions in a homogeneous shear flow with sinuous symmetry are numerically found in large-eddy simulations (LES) with no kinetic viscosity. The small-scale properties are determined by the mixing length scale $l_S$…
Bead spring models for polymers in solution are nonlinear if either the finite extensibility of the polymer, excluded volume effects or hydrodynamic interactions between polymer segments are taken into account. For such models we use a…
An analytical expression for the maximal Lyapunov exponent $\lambda_1$ in generalized Fermi-Pasta-Ulam oscillator chains is obtained. The derivation is based on the calculation of modulational instability growth rates for some unstable…
When a polymer solution is uniaxially stretched and held fixed at both ends, the solution quickly separates into droplets connected by strings and takes the beads-on-string structure. The string then becomes thinner by capillary forces.…
We study diffusion-type equations supported on structures that are randomly varying in time. After settling the issue of well-posedness, we focus on the asymptotic behavior of solutions: our main result gives sufficient conditions for…
The stability properties of one-dimensional radiative shocks with a power-law cooling function of the form $\Lambda \propto \rho^2T^\alpha$ are the main subject of this work. The linear analysis originally presented by Chevalier & Imamura,…
We develop topological methods for characterizing the relationship between polymer chain entanglement and bulk viscoelastic responses. We introduce generalized Linking Number and Writhe characteristics that are applicable to open linear…
We briefly review the recent advances in the rheology of entangled polymers and identify emerging research trends and outstanding challenges, especially with respect to branched polymers. Emphasis is placed on the role of well-characterized…
Using molecular dynamics simulations, we determine the linear and nonlinear viscoelastic properties of a model polymer melt in the unentangled regime. Several approaches are compared for the computation of linear moduli, including…
We show that viscoelastic plane Poiseuille flow becomes linearly unstable in the absence of inertia, in the limit of high elasticities, for ultra-dilute polymer solutions. While inertialess elastic instabilities have been predicted for…
Turbulence is one of the most fascinating phenomena in nature and one of the biggest challenges for modern physics. It is common knowledge that a flow of a simple, Newtonian fluid is likely to be turbulent, when velocity is high, viscosity…
Explicit expressions for the behavior of statistically isotropic composites with viscoelastic matrices and linear elastic inclusions are determined by application of the correspondence principle. The behavior of the matrix is linear in…
We extend the theory of viscosity solutions to treat scalar-valued doubly-nonlinear evolution equations. Such equations arise naturally in many mechanical models including a dry friction. After providing a suitable definition for…
General equations describing shear displacements in incompressible hyperelastic materials, holding for an arbitrary form of strain energy density function, are presented and applied to the description of nonlinear Love-type waves…
We consider a continuum model of active viscoelastic matter, whereby an active nematic liquid-crystal is coupled to a minimal model of polymer dynamics with a viscoelastic relaxation time $\tau_C$. To explore the resulting interplay between…
We study the conformation and dynamics of a single polymer chain that is pulled by a constant force applied at its one end with the other end free. Such a situation is relevant to the growing technology of manipulating individual…
We investigate the evolution of a two-phase viscoelastic material at finite strains. The phase evolution is assumed to be irreversible: One phase accretes in time in its normal direction, at the expense of the other. Mechanical response…
We have advanced our previous static theory of polymer entanglement involving an extended Cahn-Hilliard functional, to include time-dependent dynamics. We go beyond the Gaussian approximation, to the one-loop level, to compute the frequency…
Nonlinear evolution equations of the fourth order and its partial cases are derived for describing nonlinear pressure waves in a mixture liquid and gas bubbles. Influence of viscosity and heat transfer is taken into account. Exact solutions…
In this paper, we analyze the dynamics of two layers of immiscible, inviscid, incompressible, and irrotational fluids through a full nonlinear system. Our goal is to establish a virial theorem and prove the polynomial growth of slope and…