Checking the transverse Ward-Takahashi relation at one loop order in 4-dimensions

Some time ago Takahashi derived so called {\it transverse} relations relating Green's functions of different orders to complement the well-known Ward-Green-Takahashi identities of gauge theories by considering wedge rather than inner products. These transverse relations have the potential to determine the full fermion-boson vertex in terms of the renormalization functions of the fermion propagator. He & Yu have given an indicative proof at one-loop level in 4-dimensions. However, their construct involves the 4th rank Levi-Civita tensor defined only unambiguously in 4-dimensions exactly where the loop integrals diverge. Consequently, here we explicitly check the proposed transverse Ward-Takahashi relation holds at one loop order in $d$-dimensions, with $d=4+\epsilon$.Comment: 20 pages, 3 figures This version corrects and clarifies the previous result. This version has been submitted for publicatio

Random Time-Scale Invariant Diffusion and Transport Coefficients

Single particle tracking of mRNA molecules and lipid granules in living cells shows that the time averaged mean squared displacement $\overline{\delta^2}$ of individual particles remains a random variable while indicating that the particle motion is subdiffusive. We investigate this type of ergodicity breaking within the continuous time random walk model and show that $\overline{\delta^2}$ differs from the corresponding ensemble average. In particular we derive the distribution for the fluctuations of the random variable $\overline{\delta^2}$. Similarly we quantify the response to a constant external field, revealing a generalization of the Einstein relation. Consequences for the interpretation of single molecule tracking data are discussed.Comment: 4 pages, 4 figures.Article accompanied by a PRL Viewpoint in Physics1, 8 (2008

Wood-Inspired Morphologically Tunable Aligned Hydrogel for High-Performance Flexible All-Solid-State Supercapacitors

Oriented microstructures are widely found in various biological systems for multiple functions. Such anisotropic structures provide low tortuosity and sufficient surface area, desirable for the design of high-performance energy storage devices. Despite significant efforts to develop supercapacitors with aligned morphology, challenges remain due to the predefined pore sizes, limited mechanical flexibility, and low mass loading. Herein, a wood-inspired flexible all-solid-state hydrogel supercapacitor is demonstrated by morphologically tuning the aligned hydrogel matrix toward high electrode-materials loading and high areal capacitance. The highly aligned matrix exhibits broad morphological tunability (47–12 µm), mechanical flexibility (0°–180° bending), and uniform polypyrrole loading up to 7 mm thick matrix. After being assembled into a solid-state supercapacitor, the areal capacitance reaches 831 mF cm−2 for the 12 µm matrix, which is 259% times of the 47 µm matrix and 403% times of nonaligned matrix. The supercapacitor also exhibits a high energy density of 73.8 µWh cm−2, power density of 4960 µW cm−2, capacitance retention of 86.5% after 1000 cycles, and bending stability of 95% after 5000 cycles. The principle to structurally design the oriented matrices for high electrode material loading opens up the possibility for advanced energy storage applications

Radiance and Doppler shift distributions across the network of the quiet Sun

The radiance and Doppler-shift distributions across the solar network provide observational constraints of two-dimensional modeling of transition-region emission and flows in coronal funnels. Two different methods, dispersion plots and average-profile studies, were applied to investigate these distributions. In the dispersion plots, we divided the entire scanned region into a bright and a dark part according to an image of Fe xii; we plotted intensities and Doppler shifts in each bin as determined according to a filtered intensity of Si ii. We also studied the difference in height variations of the magnetic field as extrapolated from the MDI magnetogram, in and outside network. For the average-profile study, we selected 74 individual cases and derived the average profiles of intensities and Doppler shifts across the network. The dispersion plots reveal that the intensities of Si ii and C iv increase from network boundary to network center in both parts. However, the intensity of Ne viii shows different trends, namely increasing in the bright part and decreasing in the dark part. In both parts, the Doppler shift of C iv increases steadily from internetwork to network center. The average-profile study reveals that the intensities of the three lines all decline from the network center to internetwork region. The binned intensities of Si ii and Ne viii have a good correlation. We also find that the large blue shift of Ne viii does not coincide with large red shift of C iv. Our results suggest that the network structure is still prominent at the layer where Ne viii is formed in the quiet Sun, and that the magnetic structures expand more strongly in the dark part than in the bright part of this quiet Sun region.Comment: 10 pages,9 figure