2,670 research outputs found
Interpenetration as a Mechanism for Liquid-Liquid Phase Transitions
We study simple lattice systems to demonstrate the influence of
interpenetrating bond networks on phase behavior. We promote interpenetration
by using a Hamiltonian with a weakly repulsive interaction with nearest
neighbors and an attractive interaction with second-nearest neighbors. In this
way, bond networks will form between second-nearest neighbors, allowing for two
(locally) distinct networks to form. We obtain the phase behavior from analytic
solution in the mean-field approximation and exact solution on the Bethe
lattice. We compare these results with exact numerical results for the phase
behavior from grand canonical Monte Carlo simulations on square, cubic, and
tetrahedral lattices. All results show that these simple systems exhibit rich
phase diagrams with two fluid-fluid critical points and three thermodynamically
distinct phases. We also consider including third-nearest-neighbor
interactions, which give rise to a phase diagram with four critical points and
five thermodynamically distinct phases. Thus the interpenetration mechanism
provides a simple route to generate multiple liquid phases in single-component
systems, such as hypothesized in water and observed in several model and
experimental systems. Additionally, interpenetration of many such networks
appears plausible in a recently considered material made from nanoparticles
functionalized by single strands of DNA.Comment: 12 pages, 9 figures, submitted to Phys. Rev.
Transmission efficiency limit for nonlocal metalenses
The rapidly advancing capabilities in nanophotonic design are enabling
complex functionalities limited mainly by physical bounds. The efficiency of
transmission is a major consideration, but its ultimate limit remains unknown
for most systems. Here, we introduce a matrix formalism that puts a fundamental
bound on the channel-averaged transmission efficiency of any passive
multi-channel optical system based only on energy conservation and the desired
functionality, independent of the interior structure and material composition.
Applying this formalism to diffraction-limited nonlocal metalenses with a wide
field of view, we show that the transmission efficiency must decrease with the
numerical aperture for the commonly adopted designs with equal entrance and
output aperture diameters. We also show that reducing the size of the entrance
aperture can raise the efficiency bound. This work reveals a fundamental limit
on the transmission efficiency as well as providing guidance for the design of
high-efficiency multi-channel optical systems
Optimization of sharp and viewing-angle-independent structural color
Structural coloration produces some of the most brilliant colors in nature
and has many applications. However, the two competing properties of narrow
bandwidth and broad viewing angle have not been achieved simultaneously in
previous studies. Here, we use numerical optimization to discover geometries
where a sharp 7% bandwidth in scattering is achieved, yet the peak wavelength
varies less than 1%, and the peak height and peak width vary less than 6% over
broad viewing angles (0--90) under a directional illumination. Our
model system consists of dipole scatterers arranged into several rings;
interference among the scattered waves is optimized to yield the
wavelength-selective and angle-insensitive response. Such designs can be useful
for the recently proposed transparent displays that are based on
wavelength-selective scattering
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