Thermal and hydrodynamic effects in the ordering of lamellar fluids

Phase separation in a complex fluid with lamellar order has been studied in the case of cold thermal fronts propagating diffusively from external walls. The velocity hydrodynamic modes are taken into account by coupling the convection-diffusion equation for the order parameter to a generalised Navier-Stokes equation. The dynamical equations are simulated by implementing a hybrid method based on a lattice Boltzmann algorithm coupled to finite difference schemes. Simulations show that the ordering process occurs with morphologies depending on the speed of the thermal fronts or, equivalently, on the value of the thermal conductivity {\xi}. At large value of {\xi}, as in instantaneous quenching, the system is frozen in entangled configurations at high viscosity while consists of grains with well ordered lamellae at low viscosity. By decreasing the value of {\xi}, a regime with very ordered lamellae parallel to the thermal fronts is found. At very low values of {\xi} the preferred orientation is perpendicular to the walls in d = 2, while perpendicular order is lost moving far from the walls in d = 3.Comment: 8 pages, 3 figures. Accepted for publication in Phil. Trans. of Royal Soc, Ser

Regularity estimates up to the boundary for elliptic systems of difference equations

Regularity estimates up to the boundary for solutions of elliptic systems of finite difference equations were proved. The regularity estimates, obtained for boundary fitted coordinate systems on domains with smooth boundary, involve discrete Sobolev norms and are proved using pseudo-difference operators to treat systems with variable coefficients. The elliptic systems of difference equations and the boundary conditions which are considered are very general in form. The regularity of a regular elliptic system of difference equations was proved equivalent to the nonexistence of eigensolutions. The regularity estimates obtained are analogous to those in the theory of elliptic systems of partial differential equations, and to the results of Gustafsson, Kreiss, and Sundstrom (1972) and others for hyperbolic difference equations

Analysis of Dynamic Congestion Control Protocols: A Fokker-Planck Approximation

We present an approximate analysis of a queue with dynamically changing input rates that are based on implicit or explicit feedback. This is motivated by recent proposals for adaptive congestion control algorithms [RaJa 88, Jac 88], where the sender\u27s window size at the transport level is adjusted based on perceived congestion level of a bottleneck node. We develop an analysis methodology for a simplified system; yet it is powerful enough to answer the important questions regarding stability, convergence (or oscillations), fairness and the significant effect that delayed feedback plays on performance. Specifically, we find that, in the absence of feedback delay, the linear increase/exponential decrease algorithm of Jacobson and Ramakrishnan-Jain [Jac 88, RaJa 88] is provably stable and fair. Delayed feedback on the other hand, introduces oscillations for every individual user as well as unfairness across those competing for the same resource. While the simulation study of Zhang [Zha 89] and the fluid-approximation study of Bolot and Shanker [BoSh 90] have observed the oscillations in cumulative queue length and measurements by Jacobson [Jac 88] have revealed some of the unfairness properties, the reasons for these have not been identified. We identify quantitatively the cause of these effects, via-a-vis the systems parameters and properties of the algorithm used. The model presented is fairly general and can be applied to evaluate the performance of a wide range of feedback control schemes. It is an extension of the classical Fokker-Planck equation. Therefore, it addresses traffic viability (to some extent) that fluid approximation techniques do not address

THE DOMAIN DECOMPOSITION METHOD FOR MAXWELL'S EQUATIONS IN TIME DOMAIN SIMULATIONS WITH DISPERSIVE METALLIC MEDIA

The domain decomposition method based on overlapping grids is developed to solve the two-dimensional Maxwell equations in the time domain. The finite difference schemes for rectangular and polar coordinate systems are presented. Since interpolation plays a crucial role in our method, the Newton and the Fourier interpolation methods are surveyed in detail. The computational studies of the electromagnetic wave propagation in free space and the back-scattering by a perfect electric conducting object of a circular shape are performed to test the accuracy, the convergence, and the efficiency of our method. Moreover, we give a methodology to model dispersive media in time domain simulations by introducing Drude conductivity in the constitutive equations. The problem of light scattering by metallic nanoparticles is solved, and its results show that our algorithm is efficient and reliable in capturing the small scale phenomena.open

Structural Control of Metamaterial Oscillator Strength and Electric Field Enhancement at Terahertz Frequencies

The design of artificial nonlinear materials requires control over the internal resonant charge densities and local electric field distributions. We present a MM design with a structurally controllable oscillator strength and local electric field enhancement at terahertz frequencies. The MM consists of a split ring resonator (SRR) array stacked above an array of nonresonant closed conducting rings. An in-plane, lateral shift of a half unit cell between the SRR and closed ring arrays results in a decrease of the MM oscillator strength by a factor of 4 and a 40% change in the amplitude of the resonant electric field enhancement in the SRR capacitive gap. We use terahertz time-domain spectroscopy and numerical simulations to confirm our results and we propose a qualitative inductive coupling model to explain the observed electromagnetic reponse.Comment: 11 pages, 5 figure

Decoupling Crossover in Asymmetric Broadside Coupled Split Ring Resonators at Terahertz Frequencies

We investigate the electromagnetic response of asymmetric broadside coupled split ring resonators (ABC-SRRs) as a function of the relative in-plane displacement between the two component SRRs. The asymmetry is defined as the difference in the capacitive gap widths (\Delta g) between the two resonators comprising a coupled unit. We characterize the response of ABC-SRRs both numerically and experimentally via terahertz time-domain spectroscopy. As with symmetric BC-SRRs (\Delta g=0 \mu m), a large redshift in the LC resonance is observed with increasing displacement, resulting from changes in the capacitive and inductive coupling. However, for ABC-SRRs, in-plane shifting between the two resonators by more than 0.375Lo (Lo=SRR sidelength) results in a transition to a response with two resonant modes, associated with decoupling in the ABC-SRRs. For increasing \Delta g, the decoupling transition begins at the same relative shift (0.375Lo), though with an increase in the oscillator strength of the new mode. This strongly contrasts with symmetric BC-SRRs which present only one resonance for shifts up to 0.75Lo. Since all BC-SRRs are effectively asymmetric when placed on a substrate, an understanding of ABC-SRR behavior is essential for a complete understanding of BC-SRR based metamaterials

Terahertz metamaterials on free-standing highly-flexible polyimide substrates

We have fabricated resonant terahertz metamaterials on free standing polyimide substrates. The low-loss polyimide substrates can be as thin as 5.5 micron yielding robust large-area metamaterials which are easily wrapped into cylinders with a radius of a few millimeters. Our results provide a path forward for creating multi-layer non-planar metamaterials at terahertz frequencies.Comment: 4 pages, higher resolution figures available upon reques