211 research outputs found
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
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
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
One-way multigrid method in electronic structure calculations
We propose a simple and efficient one-way multigrid method for
self-consistent electronic structure calculations based on iterative
diagonalization. Total energy calculations are performed on several different
levels of grids starting from the coarsest grid, with wave functions
transferred to each finer level. The only changes compared to a single grid
calculation are interpolation and orthonormalization steps outside the original
total energy calculation and required only for transferring between grids. This
feature results in a minimal amount of code change, and enables us to employ a
sophisticated interpolation method and noninteger ratio of grid spacings.
Calculations employing a preconditioned conjugate gradient method are presented
for two examples, a quantum dot and a charged molecular system. Use of three
grid levels with grid spacings 2h, 1.5h, and h decreases the computer time by
about a factor of 5 compared to single level calculations.Comment: 10 pages, 2 figures, to appear in Phys. Rev. B, Rapid Communication
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
From colored glass condensate to gluon plasma: equilibration in high energy heavy ion collisions
The initial distribution of gluons at the very early times after a high
energy heavy ion collision is described by the bulk scale of gluon
saturation in the nuclear wavefunction. The subsequent evolution of the system
towards kinetic equilibrium is described by a non-linear Landau equation for
the single particle distributions \cite{Mueller1,Mueller2}. In this paper, we
solve this equation numerically for the idealized initial conditions proposed
by Mueller, and study the evolution of the system to equilibrium. We discuss
the sensitivity of our results on the dynamical screening of collinear
divergences. In a particular model of dynamical screening, the convergence to
the hydrodynamic limit is seen to be rapid relative to hydrodynamic time
scales. The equilibration time, the initial temperature, and the chemical
potential are shown to have a strong functional dependence on the initial gluon
saturation scale .Comment: 34 pages, 10 figure
Metamaterial-Enhanced Nonlinear Terahertz Spectroscopy
We demonstrate large nonlinear terahertz responses in the gaps of metamaterial split ring resonators in several materials and use nonlinear THz transmission and THz-pump/THz-probe spectroscopy to study the nonlinear responses and dynamics. We use the field enhancement in the SRR gaps to initiate high-field phenomena at lower incident fields. In vanadium dioxide, we drive the insulator-to-metal phase transition with high-field THz radiation. The film conductivity increases by over two orders of magnitude and the phase transition occurs on a several picosecond timescale. In gallium arsenide, we observe high-field transport phenomena, including mobility saturation and impact ionization. The carrier density increases by up to ten orders of magnitude at high fields. At the highest fields, we demonstrate THz-induced damage in both vanadium dioxide and gallium arsenide.United States. Dept. of Energy (DOE-BES, grant DE-FG02- 09ER46643)United States. Office of Naval Research (ONR Grant No. N00014-09-1-1103
- …