We consider a class of singularly perturbed delay-differential equations of the form e ’ xðtÞ 1⁄4 f ðxðtÞ; xðt rÞÞ; where r 1⁄4 rðxðtÞÞ is a state-dependent delay. We study the asymptotic shape, as e-0; of slowly oscillating periodic solutions. In particular, we show that the limiting shape of such solutions can be explicitly described by the solution of a pair of so-called max-plus equations. ...

We present a new model for bubbly cavitating flows. Based on volume-averaged equations, a subgrid model is added to account for a bubble, or multiple bubbles, within each computational cell. The model converges to the solution of ensembleaveraged bubbly flow equations for weak oscillations and monodisperse systems. In the other extreme, it also converges to the theoretical solution for a single...

We analyze two-scale Finite Element Methods for the numerical solution of elliptic homogenization problems with coefficients oscillating at a small length scale ε 1. Based on a refined two-scale regularity on the solutions, two-scale tensor product FE spaces are introduced and error estimates which are robust (i.e. independent of ε) are given. We show that under additional two-scale regularity ...

We study the convergence rate of an asymptotic expansion for the elliptic and parabolic operators with rapidly oscillating coefficients. First we propose homogenized expansions which are convolution forms of Green function and given force term of elliptic equation. Then, using local Lp-theory, the growth rate of the perturbation of Green function is found. From the representation of elliptic so...

The quasineutral limit of compressible Navier-Stokes-Poisson system with heat conductivity and general (ill-prepared) initial data is rigorously proved in this paper. It is proved that, as the Debye length tends to zero, the solution of the compressible Navier-Stokes-Poisson system converges strongly to the strong solution of the incompressible Navier-Stokes equations plus a term of fast singul...

The solution of elliptic boundary value problems often leads to singularities due to nonsmoothness of the domains on which the problem is posed. This paper studies the performance of the nonconforming hp/spectral element method for elliptic problems on non smooth domains. This paper deals with monotone singularities of type rα and rα log r as well as the oscillating singularities of type rα sin...

An old conjecture in delay equations states that Wright’s equation y(t) = −αy(t− 1)[1 + y(t)], α ∈ R has a unique slowly oscillating periodic solution (SOPS) for every parameter value α > π/2. We reformulate this conjecture and we use a method called validated continuation to rigorously compute a global continuous branch of SOPS of Wright’s equation. Using this method, we show that a part of th...

Manipulation of diblock copolymer worm micelles by external electric fields is visualized by fluorescence microscopy in dilute, aqueous solution. Hydrodynamic coupling of the poly(acrylic acid)-(1,4)-polybutadiene (PAA-PBD) worm motion to the electric field and the effective stiffening of the worms in an oscillating electric field are demonstrated. A brief discussion on using this technique to ...

Using a generalized transfer matrix method we exactly solve the Schrödinger equation in a time periodic potential, with discretized Euclidean space-time. The ground state wave function propagates in space and time with an oscillating soliton-like wave packet and the wave front is wedge shaped. In a statistical mechanics framework our solution represents the partition sum of a directed polymer s...

We describe the breathing dynamics of the self-similar core and the oscillating tails of a dispersion-managed (DM) soliton. The path-averaged propagation equation governing the shape of the DM soliton in an arbitrary dispersion map is derived. The developed theory correctly predicts the locations of the dips in the tails of the DM soliton. A general solution of the propagation equation is prese...