196 research outputs found
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
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
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
Frequency-tunable metamaterials using broadside-coupled split ring resonators
We present frequency tunable metamaterial designs at terahertz (THz)
frequencies using broadside-coupled split ring resonator (BC-SRR) arrays.
Frequency tuning, arising from changes in near field coupling, is obtained by
in-plane horizontal or vertical displacements of the two SRR layers. For
electrical excitation, the resonance frequency continuously redshifts as a
function of displacement. The maximum frequency shift occurs for displacement
of half a unit cell, with vertical displacement resulting in a shift of 663 GHz
(51% of f0) and horizontal displacement yielding a shift of 270 GHz (20% of
f0). We also discuss the significant differences in tuning that arise for
electrical excitation in comparison to magnetic excitation of BC-SRRs
Nonlinear terahertz metamaterials via field-enhanced carrier dynamics in GaAs
We demonstrate nonlinear metamaterial split ring resonators (SRRs) on GaAs at
terahertz frequencies. For SRRs on doped GaAs films, incident terahertz
radiation with peak fields of ~20 - 160 kV/cm drives intervalley scattering.
This reduces the carrier mobility and enhances the SRR LC response due to a
conductivity decrease in the doped thin film. Above ~160 kV/cm, electric field
enhancement within the SRR gaps leads to efficient impact ionization,
increasing the carrier density and the conductivity which, in turn, suppresses
the SRR resonance. We demonstrate an increase of up to 10 orders of magnitude
in the carrier density in the SRR gaps on semi-insulating GaAs substrate.
Furthermore, we show that the effective permittivity can be swept from negative
to positive values with increasing terahertz field strength in the impact
ionization regime, enabling new possibilities for nonlinear metamaterials.Comment: 5 pages, 4 figure
Metamaterial Polarization Converter Analysis: Limits of Performance
In this paper we analyze the theoretical limits of a metamaterial converter
that allows for linear-to- elliptical polarization transformation with any
desired ellipticity and ellipse orientation. We employ the transmission line
approach providing a needed level of the design generalization. Our analysis
reveals that the maximal conversion efficiency for transmission through a
single metamaterial layer is 50%, while the realistic re ection configuration
can give the conversion efficiency up to 90%. We show that a double layer
transmission converter and a single layer with a ground plane can have 100%
polarization conversion efficiency. We tested our conclusions numerically
reaching the designated limits of efficiency using a simple metamaterial
design. Our general analysis provides useful guidelines for the metamaterial
polarization converter design for virtually any frequency range of the
electromagnetic waves.Comment: 10 pages, 11 figures, 2 table
Cauchy boundaries in linearized gravitational theory
We investigate the numerical stability of Cauchy evolution of linearized
gravitational theory in a 3-dimensional bounded domain. Criteria of robust
stability are proposed, developed into a testbed and used to study various
evolution-boundary algorithms. We construct a standard explicit finite
difference code which solves the unconstrained linearized Einstein equations in
the 3+1 formulation and measure its stability properties under Dirichlet,
Neumann and Sommerfeld boundary conditions. We demonstrate the robust stability
of a specific evolution-boundary algorithm under random constraint violating
initial data and random boundary data.Comment: 23 pages including 3 figures and 2 tables, revte
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