Aspects of Floquet Bands and Topological Phase Transitions in a Continuously Driven Superlattice

Recently the creation of novel topological states of matter by a periodic driving field has attracted great attention. To motivate further experimental and theoretical studies, we investigate interesting aspects of Floquet bands and topological phase transitions in a continuously driven Harper model. In such a continuously driven system with an odd number of Floquet bands, the bands are found to have nonzero Chern numbers in general and topological phase transitions take place as we tune various system parameters, such as the amplitude or the period of the driving field. The nontrivial Floquet band topology results in a quantized transport of Wannier states in the lattice space. For certain parameter choices, very flat yet topologically nontrivial Floquet bands may also emerge, a feature that is potentially useful for the simulation of physics of strongly correlated systems. Some cases with an even number of Floquet bands may also have intriguing Dirac cones in the spectrum. Under open boundary conditions, anomalous counter-propagating chiral edge modes and degenerate zero modes are also found as the system parameters are tuned. These results should be of experimental interest because a continuously driven system is easier to realize than a periodically kicked system.Comment: 29 pages, 9 figures. Comments are welcom

The formation of acetylcholine receptor clusters visualized with quantum dots

Background: Motor innervation of skeletal muscle leads to the assembly of acetylcholine receptor (AChR) clusters in the postsynaptic membrane at the vertebrate neuromuscular junction (NMJ). Synaptic AChR aggregation, according to the diffusion-mediated trapping hypothesis, involves the establishment of a postsynaptic scaffold that "traps" freely diffusing receptors into forming high-density clusters. Although this hypothesis is widely cited to explain the formation of postsynaptic AChR clusters, direct evidence at molecular level is lacking. Results: Using quantum dots (QDs) and live cell imaging, we provide new measurements supporting the diffusion-trap hypothesis as applied to AChR cluster formation. Consistent with published works, experiments on cultured Xenopus myotomal muscle cells revealed that AChRs at clusters that formed spontaneously (pre-patterned clusters, also called hot spots) and at those induced by nerve-innervation or by growth factor-coated latex beads were very stable whereas diffuse receptors outside these regions were mobile. Moreover, despite the restriction of AChR movement at sites of synaptogenic stimulation, individual receptors away from these domains continued to exhibit free diffusion, indicating that AChR clustering at NMJ does not involve an active attraction of receptors but is passive and diffusion-driven. Conclusion: Single-molecular tracking using QDs has provided direct evidence that the clustering of AChRs in muscle cells in response to synaptogenic stimuli is achieved by two distinct cellular processes: the Brownian motion of receptors in the membrane and their trapping and immobilization at the synaptic specialization. This study also provides a clearer picture of the "trap" that it is not a uniformly sticky area but consists of discrete foci at which AChRs are immobilized

Crosslinking-induced endocytosis of acetylcholine receptors by quantum dots

In a majority of patients with myasthenia gravis (MG), anti-acetylcholine receptor (AChR) antibodies target postsynaptic AChR clusters and thus compromise the membrane integrity of neuromuscular junctions (NMJs) and lead to muscle weakness. Antibody-induced endocytosis of AChRs in the postsynaptic membrane represents the initial step in the pathogenesis of MG; however, the molecular mechanisms underlying AChR endocytosis remain largely unknown. Here, we developed an approach to mimic the pathogenic antibodies for inducing the crosslinking and internalization of AChRs from the postsynaptic membrane. Using biotin-α-bungarotoxin and quantum dot (QD)-streptavidin, cell-surface and internalized AChRs could be readily distinguished by comparing the size, fluorescence intensity, trajectory, and subcellular localization of the QD signals. QD-induced AChR endocytosis was mediated by clathrin-dependent and caveolin-independent mechanisms, and the trafficking of internalized AChRs in the early endosomes required the integrity of microtubule structures. Furthermore, activation of the agrin/MuSK (muscle-specific kinase) signaling pathway strongly suppressed QD-induced internalization of AChRs. Lastly, QD-induced AChR crosslinking potentiated the dispersal of aneural AChR clusters upon synaptic induction. Taken together, our results identify a novel approach to study the mechanisms of AChR trafficking upon receptor crosslinking and endocytosis, and demonstrate that agrin-MuSK signaling pathways protect against crosslinking-induced endocytosis of AChRs. © 2014 Lee et al.published_or_final_versio

Structural Color 3D Printing By Shrinking Photonic Crystals

The rings, spots and stripes found on some butterflies, Pachyrhynchus weevils, and many chameleons are notable examples of natural organisms employing photonic crystals to produce colorful patterns. Despite advances in nanotechnology, we still lack the ability to print arbitrary colors and shapes in all three dimensions at this microscopic length scale. Commercial nanoscale 3D printers based on two-photon polymerization are incapable of patterning photonic crystal structures with the requisite ~300 nm lattice constant to achieve photonic stopbands/ bandgaps in the visible spectrum and generate colors. Here, we introduce a means to produce 3D-printed photonic crystals with a 5x reduction in lattice constants (periodicity as small as 280 nm), achieving sub-100-nm features with a full range of colors. The reliability of this process enables us to engineer the bandstructures of woodpile photonic crystals that match experiments, showing that observed colors can be attributed to either slow light modes or stopbands. With these lattice structures as 3D color volumetric elements (voxels), we printed 3D microscopic scale objects, including the first multi-color microscopic model of the Eiffel Tower measuring only 39-microns tall with a color pixel size of 1.45 microns. The technology to print 3D structures in color at the microscopic scale promises the direct patterning and integration of spectrally selective devices, such as photonic crystal-based color filters, onto free-form optical elements and curved surfaces

Development of a Respirable Dust Mitigation System for a High Longwall Face at Sihe Colliery in China – a Case Study

Dust is a major hazard in underground coal mines that threatens the work health and safety of coal miners. The dust issue becomes increasingly significant with the development of highly mechanized coal mining. This issue is particularly serious at the high longwall faces of the Sihe colliery in China as the concentration of dust, in particular respirable dust, at these faces far exceeds the regulatory dust limits. Field testing and computational fluid dynamics (CFD) simulations were conducted to understand the sources of dust generation and its dynamic movement in the #5301 longwall face of high-cutting height at the colliery. The investigation results showed that shearer generated dust was minimal during the coal cutting operation; that face spalling and chock movement were the main dust generating sources, causing significant contamination to the walkway; and that the majority of dust particles from the face (regardless of source) eventually disperse into the main gate, where the dust concentration was greater than 500 mg/m3. These findings were used to develop an effective coal dust mitigation system involving the installation of dust scrubbers, curtains, and venture and crescent sprays. The results of CFD modeling indicate that the dust concentration could be significantly reduced by adopting the new dust mitigation system

Ocean-related global change alters lipid biomarker production in common marine phytoplankton

Lipids, in their function as trophic markers in food webs and organic matter source indicators in the water column and sediments, provide a tool for reconstructing the complexity of global change effects on aquatic ecosystems. It remains unclear how ongoing changes in multiple environmental drivers affect the production of key lipid biomarkers in marine phytoplankton. Here, we tested the responses of sterols, alkenones and fatty acids (FAs) in the diatom Phaeodactylum tricornutum, the cryptophyte Rhodomonas sp. and the haptophyte Emiliania huxleyi under a full-factorial combination of three temperatures (12, 18 and 24 ∘C), three N : P supply ratios (molar ratios 10 : 1, 24 : 1 and 63 : 1) and two pCO2 levels (560 and 2400 µatm) in semicontinuous culturing experiments. Overall, N and P deficiency had a stronger effect on per-cell contents of sterols, alkenones and FAs than warming and enhanced pCO2. Specifically, P deficiency caused an overall increase in biomarker production in most cases, while N deficiency, warming and high pCO2 caused nonsystematic changes. Under future ocean scenarios, we predict an overall decrease in carbon-normalized contents of sterols and polyunsaturated fatty acids (PUFAs) in E. huxleyi and P. tricornutum and a decrease in sterols but an increase in PUFAs in Rhodomonas sp. Variable contents of lipid biomarkers indicate a diverse carbon allocation between marine phytoplankton species in response to changing environments. Thus, it is necessary to consider the changes in key lipids and their consequences for food-web dynamics and biogeochemical cycles, when predicting the influence of global change on marine ecosystems

Asymptotic Behavior of Ext functors for modules of finite complete intersection dimension

Let $R$ be a local ring, and let $M$ and $N$ be finitely generated $R$-modules such that $M$ has finite complete intersection dimension. In this paper we define and study, under certain conditions, a pairing using the modules \Ext_R^i(M,N) which generalizes Buchweitz's notion of the Herbrand diference. We exploit this pairing to examine the number of consecutive vanishing of \Ext_R^i(M,N) needed to ensure that \Ext_R^i(M,N)=0 for all $i\gg 0$. Our results recover and improve on most of the known bounds in the literature, especially when $R$ has dimension at most two