On the corrections to Strong-Stretching Theory for end-confined, charged polymers in a uniform electric field

We investigate the properties of a system of semi-diluted polymers in the presence of charged groups and counter-ions, by means of self-consistent field theory. We study a system of polyelectrolyte chains grafted to a similarly, as well as an oppositely charged surface, solving a set of saddle-point equations that couple the modified diffusion equation for the polymer partition function to the Poisson-Boltzmann equation describing the charge distribution in the system. A numerical study of this set of equations is presented and comparison is made with previous studies. We then consider the case of semi-diluted, grafted polymer chains in the presence of charge-end-groups. We study the problem with self-consistent field as well as strong-stretching theory. We derive the corrections to the Milner-Witten-Cates (MWC) theory for weakly charged chains and show that the monomer-density deviates from the parabolic profile expected in the uncharged case. The corresponding corrections are shown to be dictated by an Abel-Volterra integral equation of the second kind. The validity of our theoretical findings is confirmed comparing the predictions with the results obtained within numerical self-consistent field theory.Comment: 15 Pages, 12 figure

Motion of Contact Line of a Crystal Over the Edge of Solid Mask in Epitaxial Lateral Overgrowth

Mathematical model that allows for direct tracking of the homoepitaxial crystal growth out of the window etched in the solid, pre-deposited layer on the substrate is described. The growth is governed by the normal (to the crystal-vapor interface) flux from the vapor phase and by the interface diffusion. The model accounts for possibly inhomogeneous energy of the mask surface and for strong anisotropies of crystal-vapor interfacial energy and kinetic mobility. Results demonstrate that the motion of the crystal-mask contact line slows down abruptly as radius of curvature of the mask edge approaches zero. Numerical procedure is suggested to overcome difficulties associated with ill-posedness of the evolution problem for the interface with strong energy anisotropy. Keywords: Thin films, epitaxy, MOCVD, surface diffusion, interface dynamics, contact lines, rough surfaces, wetting, regularization of ill-posed evolution problems.Comment: 21 pages, 11 figures; to appear in Computational Materials Scienc

Generation of interface for an Allen-Cahn equation with nonlinear diffusion

In this note, we consider a nonlinear diffusion equation with a bistable reaction term arising in population dynamics. Given a rather general initial data, we investigate its behavior for small times as the reaction coefficient tends to infinity: we prove a generation of interface property

Spectral collocation methods

This review covers the theory and application of spectral collocation methods. Section 1 describes the fundamentals, and summarizes results pertaining to spectral approximations of functions. Some stability and convergence results are presented for simple elliptic, parabolic, and hyperbolic equations. Applications of these methods to fluid dynamics problems are discussed in Section 2

Statistical stability in time reversal

When a signal is emitted from a source, recorded by an array of transducers, time reversed and re-emitted into the medium, it will refocus approximately on the source location. We analyze the refocusing resolution in a high frequency, remote sensing regime, and show that, because of multiple scattering, in an inhomogeneous or random medium it can improve beyond the diffraction limit. We also show that the back-propagated signal from a spatially localized narrow-band source is self-averaging, or statistically stable, and relate this to the self-averaging properties of functionals of the Wigner distribution in phase space. Time reversal from spatially distributed sources is self-averaging only for broad-band signals. The array of transducers operates in a remote-sensing regime so we analyze time reversal with the parabolic or paraxial wave equation

Maxwell-Drude-Bloch dissipative few-cycle optical solitons

We study the propagation of few-cycle pulses in two-component medium consisting of nonlinear amplifying and absorbing two-level centers embedded into a linear and conductive host material. First we present a linear theory of propagation of short pulses in a purely conductive material, and demonstrate the diffusive behavior for the evolution of the low-frequency components of the magnetic field in the case of relatively strong conductivity. Then, numerical simulations carried out in the frame of the full nonlinear theory involving the Maxwell-Drude-Bloch model reveal the stable creation and propagation of few-cycle dissipative solitons under excitation by incident femtosecond optical pulses of relatively high energies. The broadband losses that are introduced by the medium conductivity represent the main stabilization mechanism for the dissipative few-cycle solitons.Comment: 38 pages, 10 figures. submitted to Physical Review