Spectral solver for Cauchy problems in polar coordinates using discrete Hankel transforms

We introduce a Fourier-Bessel-based spectral solver for Cauchy problems featuring Laplacians in polar coordinates under homogeneous Dirichlet boundary conditions. We use FFTs in the azimuthal direction to isolate angular modes, then perform discrete Hankel transform (DHT) on each mode along the radial direction to obtain spectral coefficients. The two transforms are connected via numerical and cardinal interpolations. We analyze the boundary-dependent error bound of DHT; the worst case is $\sim N^{-3/2}$, which governs the method, and the best $\sim e^{-N}$, which then the numerical interpolation governs. The complexity is $O[N^3]$. Taking advantage of Bessel functions being the eigenfunctions of the Laplacian operator, we solve linear equations for all times. For non-linear equations, we use a time-splitting method to integrate the solutions. We show examples and validate the method on the two-dimensional wave equation, which is linear, and on two non-linear problems: a time-dependent Poiseuille flow and the flow of a Bose-Einstein condensate on a disk

Effect of Fish Oil on Enteritis Damage and Intestinal Gene Expression Profiles in Vibrio parahaemolyticus Infected Mice

Fish oil (FO) can modulate the gut ecosystem and improve intestinal health, but the specific role and mechanism of FO in preventing foodborne pathogen infection are still unclear. In this study, the effect of FO on enteritis damage and intestinal gene expression profiles in Vibrio parahaemolyticus (Vp) infected mice was investigated. The disease activity index (DAI) score, the colonic histopathological score (HIS), the expression of intestinal fibrosis biomarkers (type I and type III collagen), the contents of the cytokines interleukin-1β (IL-1β), interleukin-6 (IL-6) and tumor necrosis factor-α (TNFα), the activities of the antioxidant enzymes catalase (AT), superoxide dismutase (SOD) and total antioxidant enzymes (TAE) and the colonic gene expression profiles in the mouse model of Vp infection were measured before and after FO intervention. The results showed that gavage with 4.0 mg/d FO significantly reduced DAI scores and HIS, and alleviated colonic pathological damage. FO could also significantly down-regulate the expression of intestinal fibrosis-related proteins (P < 0.05), maintain intestinal barrier functions, and inhibit cytokine-mediated excessive inflammation and oxidative stress. Thus, FO reduced body damage induced by Vp infection by altering the gene expression pattern in the colon, up-regulating the gene expression of peroxisome proliferator activated receptor (PPAR), enriching the PPAR signaling pathway, and inhibiting the nuclear factor-κB signaling pathway. Hence, dietary supplementation of FO can protect the body against foodborne pathogens

Long-distance propagation of high-velocity antiferromagnetic spin waves

We report on coherent propagation of antiferromagnetic (AFM) spin waves over a long distance ($\sim$10 $\mu$m) at room temperature in a canted AFM $\alpha$-Fe$_2$O$_3$ with the Dzyaloshinskii-Moriya interaction (DMI). Unprecedented high group velocities (up to 22.5 km/s) are characterized by microwave transmission using all-electrical spin wave spectroscopy. We derive analytically AFM spin-wave dispersion in the presence of the DMI which accounts for our experimental results. The AFM spin waves excited by nanometric coplanar waveguides with large wavevectors enter the exchange regime and follow a quasi-linear dispersion relation. Fitting of experimental data with our theoretical model yields an AFM exchange stiffness length of 1.7 angstrom. Our results provide key insights on AFM spin dynamics and demonstrate high-speed functionality for AFM magnonics

Dynamical Axion Field in Topological Magnetic Insulators

Axions are very light, very weakly interacting particles postulated more than 30 years ago in the context of the Standard Model of particle physics. Their existence could explain the missing dark matter of the universe. However, despite intensive searches, they have yet to be detected. In this work, we show that magnetic fluctuations of topological insulators couple to the electromagnetic fields exactly like the axions, and propose several experiments to detect this dynamical axion field. In particular, we show that the axion coupling enables a nonlinear modulation of the electromagnetic field, leading to attenuated total reflection. We propose a novel optical modulators device based on this principle.Comment: 5 pages, 3 figure

Optimal Path for Controlling Sectoral CO2 Emissions Among China’s Regions: A Centralized DEA Approach

This paper proposes a centralized data envelopment analysis (DEA) model for industrial optimization based on several different production technologies among several regions. We developed this model based on improved Kuosmanen environmental DEA technology, which avoids positive shadow price on undesirable outputs. We also designed a dual model for our centralized DEA model, and used it to analyze shadow prices on CO2 emissions. We further employed the proposed model to determine the optimal path for controlling CO2 emissions at the sector level for each province in China. At sectoral level, manufacturing showed the highest potential emissions reduction, and transportation was the largest accepter of emission quotas. At regional level, western and northeastern areas faced the largest adjustments in allowable emissions, while central and eastern areas required the least amount of adjustment. Because our model represents increase or decrease in emissions bidirectionally in terms of shadow price analysis, this setting makes the shadow price on CO2 emissions lower than strong regulation (decreasing CO2 emissions along with increasing value added) used by directional distance function (DDF)

Frustrated Lewis Pair Catalysed Reactions

In recent years, frustrated Lewis pairs have been widely used in small molecules activation and catalytic transformations. This graphic review is aimed to provide the fundamental understanding of frustrated Lewis pair reactivity and the exploitation thereof in catalytic reactions