Geometric Aspects of Ambrosetti-Prodi operators with Lipschitz nonlinearities

For Dirichlet boundary conditions on a bounded domain, what happens to the critical set of the Ambrosetti-Prodi operator if the nonlinearity is only a Lipschitz map? It turns out that many properties which hold in the smooth case are preserved, despite of the fact that the operator is not even differentiable at some points. In particular, a global Lyapunov-Schmidt decomposition of great convenience for numerical inversion is still available

Electronic Liquid Crystal Phases of a Doped Mott Insulator

The character of the ground state of an antiferromagnetic insulator is fundamentally altered upon addition of even a small amount of charge. The added charges agglomerate along domain walls at which the spin correlations, which may or may not remain long-ranged, suffer a $\pi$ phase shift. In two dimensions, these domain walls are ``stripes'' which are either insulating, or conducting, i.e. metallic rivers with their own low energy degrees of freedom. However, quasi one-dimensional metals typically undergo a transition to an insulating ordered charge density wave (CDW) state at low temperatures. Here it is shown that such a transition is eliminated if the zero-point energy of transverse stripe fluctuations is sufficiently large in comparison to the CDW coupling between stripes. As a consequence, there exist novel, liquid-crystalline low-temperature phases -- an electron smectic, with crystalline order in one direction, but liquid-like correlations in the other, and an electron nematic with orientational order but no long-range positional order. These phases, which constitute new states of matter, can be either high temperature supeconductors or two-dimensional anisotropic ``metallic'' non-Fermi liquids. Evidence for the new phases may already have been obtained by neutron scattering experiments in the cuprate superconductor, La_{1.6-x}Nd_{0.4}Sr_xCuO_{4}.Comment: 5 pages in RevTex with two figures in ep

Syntaxin 16 is a master recruitment factor for cytokinesis

Recently it was shown that both recycling endosome and endosomal sorting complex required for transport (ESCRT) components are required for cytokinesis, in which they are believed to act in a sequential manner to bring about secondary ingression and abscission, respectively. However, it is not clear how either of these complexes is targeted to the midbody and whether their delivery is coordinated. The trafficking of membrane vesicles between different intracellular organelles involves the formation of soluble N-ethylmalei­mide–sensitive factor attachment protein receptor (SNARE) complexes. Although membrane traffic is known to play an important role in cytokinesis, the contribution and identity of intracellular SNAREs to cytokinesis remain unclear. Here we demonstrate that syntaxin 16 is a key regulator of cytokinesis, as it is required for recruitment of both recycling endosome–associated Exocyst and ESCRT machinery during late telophase, and therefore that these two distinct facets of cytokinesis are inextricably linked

Topological Quantum Phase Transition in Synthetic Non-Abelian Gauge Potential

The method of synthetic gauge potentials opens up a new avenue for our understanding and discovering novel quantum states of matter. We investigate the topological quantum phase transition of Fermi gases trapped in a honeycomb lattice in the presence of a synthetic non- Abelian gauge potential. We develop a systematic fermionic effective field theory to describe a topological quantum phase transition tuned by the non-Abelian gauge potential and ex- plore its various important experimental consequences. Numerical calculations on lattice scales are performed to compare with the results achieved by the fermionic effective field theory. Several possible experimental detection methods of topological quantum phase tran- sition are proposed. In contrast to condensed matter experiments where only gauge invariant quantities can be measured, both gauge invariant and non-gauge invariant quantities can be measured by experimentally generating various non-Abelian gauges corresponding to the same set of Wilson loops

Lattice Boltzmann simulations in microfluidics: probing the no-slip boundary condition in hydrophobic, rough, and surface nanobubble laden microchannels

In this contribution we review recent efforts on investigations of the effect of (apparent) boundary slip by utilizing lattice Boltzmann simulations. We demonstrate the applicability of the method to treat fundamental questions in microfluidics by investigating fluid flow in hydrophobic and rough microchannels as well as over surfaces covered by nano- or microscale gas bubbles.Comment: 11 pages, 6 figure

Dual-gated bilayer graphene hot electron bolometer

Detection of infrared light is central to diverse applications in security, medicine, astronomy, materials science, and biology. Often different materials and detection mechanisms are employed to optimize performance in different spectral ranges. Graphene is a unique material with strong, nearly frequency-independent light-matter interaction from far infrared to ultraviolet, with potential for broadband photonics applications. Moreover, graphene's small electron-phonon coupling suggests that hot-electron effects may be exploited at relatively high temperatures for fast and highly sensitive detectors in which light energy heats only the small-specific-heat electronic system. Here we demonstrate such a hot-electron bolometer using bilayer graphene that is dual-gated to create a tunable bandgap and electron-temperature-dependent conductivity. The measured large electron-phonon heat resistance is in good agreement with theoretical estimates in magnitude and temperature dependence, and enables our graphene bolometer operating at a temperature of 5 K to have a low noise equivalent power (33 fW/Hz1/2). We employ a pump-probe technique to directly measure the intrinsic speed of our device, >1 GHz at 10 K.Comment: 5 figure

Graphene plasmonics

Two rich and vibrant fields of investigation, graphene physics and plasmonics, strongly overlap. Not only does graphene possess intrinsic plasmons that are tunable and adjustable, but a combination of graphene with noble-metal nanostructures promises a variety of exciting applications for conventional plasmonics. The versatility of graphene means that graphene-based plasmonics may enable the manufacture of novel optical devices working in different frequency ranges, from terahertz to the visible, with extremely high speed, low driving voltage, low power consumption and compact sizes. Here we review the field emerging at the intersection of graphene physics and plasmonics.Comment: Review article; 12 pages, 6 figures, 99 references (final version available only at publisher's web site

Application of Graphene within Optoelectronic Devices and Transistors

Scientists are always yearning for new and exciting ways to unlock graphene's true potential. However, recent reports suggest this two-dimensional material may harbor some unique properties, making it a viable candidate for use in optoelectronic and semiconducting devices. Whereas on one hand, graphene is highly transparent due to its atomic thickness, the material does exhibit a strong interaction with photons. This has clear advantages over existing materials used in photonic devices such as Indium-based compounds. Moreover, the material can be used to 'trap' light and alter the incident wavelength, forming the basis of the plasmonic devices. We also highlight upon graphene's nonlinear optical response to an applied electric field, and the phenomenon of saturable absorption. Within the context of logical devices, graphene has no discernible band-gap. Therefore, generating one will be of utmost importance. Amongst many others, some existing methods to open this band-gap include chemical doping, deformation of the honeycomb structure, or the use of carbon nanotubes (CNTs). We shall also discuss various designs of transistors, including those which incorporate CNTs, and others which exploit the idea of quantum tunneling. A key advantage of the CNT transistor is that ballistic transport occurs throughout the CNT channel, with short channel effects being minimized. We shall also discuss recent developments of the graphene tunneling transistor, with emphasis being placed upon its operational mechanism. Finally, we provide perspective for incorporating graphene within high frequency devices, which do not require a pre-defined band-gap.Comment: Due to be published in "Current Topics in Applied Spectroscopy and the Science of Nanomaterials" - Springer (Fall 2014). (17 pages, 19 figures