Galerkin FEM for fractional order parabolic equations with initial data in H−s, 0<s≤1H^{-s},~0 < s \le 1

We investigate semi-discrete numerical schemes based on the standard Galerkin and lumped mass Galerkin finite element methods for an initial-boundary value problem for homogeneous fractional diffusion problems with non-smooth initial data. We assume that $\Omega\subset \mathbb{R}^d$, $d=1,2,3$ is a convex polygonal (polyhedral) domain. We theoretically justify optimal order error estimates in $L_2$- and $H^1$-norms for initial data in $H^{-s}(\Omega),~0\le s \le 1$. We confirm our theoretical findings with a number of numerical tests that include initial data $v$ being a Dirac $\delta$-function supported on a $(d-1)$-dimensional manifold.Comment: 13 pages, 3 figure

Phase dynamics of inductively coupled intrinsic Josephson junctions and terahertz electromagnetic radiation

The Josephson effects associated with quantum tunneling of Cooper pairs manifest as nonlinear relations between the superconductivity phase difference and the bias current and voltage. Many novel phenomena appear, such as Shapiro steps in dc cuurent-voltage (IV) characteristics of a Josephson junction under microwave shining, which can be used as a voltage standard. Inversely, the Josephson effects provide a unique way to generate high-frequency electromagnetic (EM) radiation by dc bias voltage. The discovery of cuprate high-Tc superconductors accelerated the effort to develop novel source of EM waves based on a stack of atomically dense-packed intrinsic Josephson junctions (IJJs), since the large superconductivity gap covers the whole terahertz frequency band. Very recently, strong and coherent terahertz radiations have been successfully generated from a mesa structure of $\rm{Bi_2Sr_2CaCu_2O_{8+\delta}}$ single crystal which works both as the source of energy gain and as the cavity for resonance. It is then found theoretically that, due to huge inductive coupling of IJJs produced by the nanometer junction separation and the large London penetration depth of order of $\rm{\mu m}$ of the material, a novel dynamic state is stabilized in the coupled sine-Gordon system, in which $\pm \pi$ kinks in phase differences are developed responding to the standing wave of Josephson plasma and are stacked alternatively in the c-axis. This novel solution of the inductively coupled sine-Gordon equations captures the important features of experimental observations. The theory predicts an optimal radiation power larger than the one available to date by orders of magnitude, and thus suggests the technological relevance of the phenomena.Comment: review article (69 pages, 30 figures

Ventricular divergence correlates with epicardial wavebreaks and predicts ventricular arrhythmia in isolated rabbit hearts during therapeutic hypothermia

INTRODUCTION: High beat-to-beat morphological variation (divergence) on the ventricular electrogram during programmed ventricular stimulation (PVS) is associated with increased risk of ventricular fibrillation (VF), with unclear mechanisms. We hypothesized that ventricular divergence is associated with epicardial wavebreaks during PVS, and that it predicts VF occurrence. METHOD AND RESULTS: Langendorff-perfused rabbit hearts (n = 10) underwent 30-min therapeutic hypothermia (TH, 30°C), followed by a 20-min treatment with rotigaptide (300 nM), a gap junction modifier. VF inducibility was tested using burst ventricular pacing at the shortest pacing cycle length achieving 1:1 ventricular capture. Pseudo-ECG (p-ECG) and epicardial activation maps were simultaneously recorded for divergence and wavebreaks analysis, respectively. A total of 112 optical and p-ECG recordings (62 at TH, 50 at TH treated with rotigaptide) were analyzed. Adding rotigaptide reduced ventricular divergence, from 0.13±0.10 at TH to 0.09±0.07 (p = 0.018). Similarly, rotigaptide reduced the number of epicardial wavebreaks, from 0.59±0.73 at TH to 0.30±0.49 (p = 0.036). VF inducibility decreased, from 48±31% at TH to 22±32% after rotigaptide infusion (p = 0.032). Linear regression models showed that ventricular divergence correlated with epicardial wavebreaks during TH (p<0.001). CONCLUSION: Ventricular divergence correlated with, and might be predictive of epicardial wavebreaks during PVS at TH. Rotigaptide decreased both the ventricular divergence and epicardial wavebreaks, and reduced the probability of pacing-induced VF during TH

Composite Polarons in Ferromagnetic Narrow-band Metallic Manganese Oxides

A new mechanism is proposed to explain the colossal magnetoresistance and related phenomena. Moving electrons accompanied by Jahn-Teller phonon and spin-wave clouds may form composite polarons in ferromagnetic narrow-band manganites. The ground-state and finite-temperature properties of such composite polarons are studied in the present paper. By using a variational method, it is shown that the energy of the system at zero temperature decreases with the formation of composite polaron; the energy spectrum and effective mass of the composite polaron at finite temperature is found to be strongly renormalized by the temperature and the magnetic field. It is suggested that the composite polaron contribute significantly to the transport and the thermodynamic properties in ferromagnetic narrow-band metallic manganese oxides.Comment: Latex, no figur

Controlled Synthesis of Organic/Inorganic van der Waals Solid for Tunable Light-matter Interactions

Van der Waals (vdW) solids, as a new type of artificial materials that consist of alternating layers bonded by weak interactions, have shed light on fascinating optoelectronic device concepts. As a result, a large variety of vdW devices have been engineered via layer-by-layer stacking of two-dimensional materials, although shadowed by the difficulties of fabrication. Alternatively, direct growth of vdW solids has proven as a scalable and swift way, highlighted by the successful synthesis of graphene/h-BN and transition metal dichalcogenides (TMDs) vertical heterostructures from controlled vapor deposition. Here, we realize high-quality organic and inorganic vdW solids, using methylammonium lead halide (CH3NH3PbI3) as the organic part (organic perovskite) and 2D inorganic monolayers as counterparts. By stacking on various 2D monolayers, the vdW solids behave dramatically different in light emission. Our studies demonstrate that h-BN monolayer is a great complement to organic perovskite for preserving its original optical properties. As a result, organic/h-BN vdW solid arrays are patterned for red light emitting. This work paves the way for designing unprecedented vdW solids with great potential for a wide spectrum of applications in optoelectronics

Inhibition of gap junctional Intercellular communication in WB-F344 rat liver epithelial cells by triphenyltin chloride through MAPK and PI3-kinase pathways

<p>Abstract</p> <p>Background</p> <p>Organotin compounds (OTCs) have been widely used as stabilizers in the production of plastic, agricultural pesticides, antifoulant plaints and wood preservation. The toxicity of triphenyltin (TPT) compounds was known for their embryotoxic, neurotoxic, genotoxic and immunotoxic effects in mammals. The carcinogenicity of TPT was not well understood and few studies had discussed the effects of OTCs on gap junctional intercellular communication (GJIC) of cells.</p> <p>Method</p> <p>In the present study, the effects of triphenyltin chloride (TPTC) on GJIC in WB-F344 rat liver epithelial cells were evaluated, using the scrape-loading dye transfer technique.</p> <p>Results</p> <p>TPTC inhibited GJIC after a 30-min exposure in a concentration- and time-dependent manner. Pre-incubation of cells with the protein kinase C (PKC) inhibitor did not modify the response, but the specific MEK 1 inhibitor PD98059 and PI3K inhibitor LY294002 decreased substantially the inhibition of GJIC by TPTC. After WB-F344 cells were exposed to TPTC, phosphorylation of Cx43 increased as seen in Western blot analysis.</p> <p>Conclusions</p> <p>These results show that TPTC inhibits GJIC in WB-F344 rat liver epithelial cells by altering the Cx43 protein expression through both MAPK and PI3-kinase pathways.</p

Linear-Time Algorithms for Computing Maximum-Density Sequence Segments with Bioinformatics Applications

We study an abstract optimization problem arising from biomolecular sequence analysis. For a sequence A of pairs (a_i,w_i) for i = 1,..,n and w_i>0, a segment A(i,j) is a consecutive subsequence of A starting with index i and ending with index j. The width of A(i,j) is w(i,j) = sum_{i <= k <= j} w_k, and the density is (sum_{i<= k <= j} a_k)/ w(i,j). The maximum-density segment problem takes A and two values L and U as input and asks for a segment of A with the largest possible density among those of width at least L and at most U. When U is unbounded, we provide a relatively simple, O(n)-time algorithm, improving upon the O(n \log L)-time algorithm by Lin, Jiang and Chao. When both L and U are specified, there are no previous nontrivial results. We solve the problem in O(n) time if w_i=1 for all i, and more generally in O(n+n\log(U-L+1)) time when w_i>=1 for all i.Comment: 23 pages, 13 figures. A significant portion of these results appeared under the title, "Fast Algorithms for Finding Maximum-Density Segments of a Sequence with Applications to Bioinformatics," in Proceedings of the Second Workshop on Algorithms in Bioinformatics (WABI), volume 2452 of Lecture Notes in Computer Science (Springer-Verlag, Berlin), R. Guigo and D. Gusfield editors, 2002, pp. 157--17