Characteristic length of a Holographic Superconductor with dd-wave gap

After the discovery of the $s$-wave and $p$-wave holographic superconductors, holographic models of $d$-wave superconductor have also been constructed recently. We study analytically the perturbation of the dual gravity theory to calculate the superconducting coherence length $\xi$ of the $d$-wave holographic superconductor near the superconducting phase transition point. The superconducting coherence length $\xi$ divergents as $(1-T/T_c)^{-1/2}$ near the critical temperature $T_c$. We also obtain the magnetic penetration depth $\lambda\propto(T_c-T)^{-1/2}$ by adding a small external homogeneous magnetic field. The results agree with the $s$-wave and $p$-wave models, which are also the same as the Ginzburg-Landau theory.Comment: last version, 10 pages, accepted by PR

Relaxation Oscillation Profile of Limit Cycle in Predator-Prey System

It is known that some predator-prey system can possess a unique limit cycle which is globally asymptotically stable. For a prototypical predator-prey system, we show that the solution curve of the limit cycle exhibits temporal patterns of a relaxation oscillator, or a Heaviside function, when certain parameter is small

A Novel Apex-Time Network for Cross-Dataset Micro-Expression Recognition

The automatic recognition of micro-expression has been boosted ever since the successful introduction of deep learning approaches. As researchers working on such topics are moving to learn from the nature of micro-expression, the practice of using deep learning techniques has evolved from processing the entire video clip of micro-expression to the recognition on apex frame. Using the apex frame is able to get rid of redundant video frames, but the relevant temporal evidence of micro-expression would be thereby left out. This paper proposes a novel Apex-Time Network (ATNet) to recognize micro-expression based on spatial information from the apex frame as well as on temporal information from the respective-adjacent frames. Through extensive experiments on three benchmarks, we demonstrate the improvement achieved by learning such temporal information. Specially, the model with such temporal information is more robust in cross-dataset validations.Comment: 6 pages, 3 figures, 3 tables, code available, accepted in ACII 201

Time-dependent energetic proton acceleration and scaling laws in ultra-intense laser pulses interactions with thin foils

A two-phase model, where the plasma expansion is an isothermal one when laser irradiates and a following adiabatic one after laser ends, has been proposed to predict the maximum energy of the proton beams induced in the ultra-intense laser-foil interactions. The hot-electron recirculation in the ultra-intense laser-solid interactions has been accounted in and described by the time-dependent hot-electron density continuously in this model. The dilution effect of electron density as electrons recirculate and spread laterally has been considered. With our model, the scaling laws of maximum ion energy have been achieved and the dependence of the scaling coefficients on laser intensity, pulse duration and target thickness have been obtained. Some interesting results have been predicted: the adiabatic expansion is an important process of the ion acceleration and cannot be neglected; the whole acceleration time is about 10-20 times of laser pulse duration; the larger the laser intensity, the more sensitive the maximum ion energy to the change of focus radius, and so on.Comment: 15 pages, 4 figures, submitted to PR

Measuring Electric Charge and Molecular Coverage on Electrode Surface from Transient Induced Molecular Electronic Signal (TIMES).

Charge density and molecular coverage on the surface of electrode play major roles in the science and technology of surface chemistry and biochemical sensing. However, there has been no easy and direct method to characterize these quantities. By extending the method of Transient Induced Molecular Electronic Signal (TIMES) which we have used to measure molecular interactions, we are able to quantify the amount of charge in the double layers at the solution/electrode interface for different buffer strengths, buffer types, and pH values. Most uniquely, such capabilities can be applied to study surface coverage of immobilized molecules. As an example, we have measured the surface coverage for thiol-modified single-strand deoxyribonucleic acid (ssDNA) as anchored probe and 6-Mercapto-1-hexanol (MCH) as blocking agent on the platinum surface. Through these experiments, we demonstrate that TIMES offers a simple and accurate method to quantify surface charge and coverage of molecules on a metal surface, as an enabling tool for studies of surface properties and surface functionalization for biochemical sensing and reactions

Supercurrent in p-wave Holographic Superconductor

The p-wave and $p+ip$-wave holographic superconductors with fixed DC supercurrent are studied by introducing a non-vanishing vector potential. We find that close to the critical temperature $T_c$ of zero current, the numerical results of both the p wave model and the $p+ip$ model are the same as those of Ginzburg-Landau (G-L) theory, for example, the critical current $j_c \sim (T_c-T)^{3/2}$ and the phase transition in the presence of a DC current is a first order transition. Besides the similar results between both models, the $p+ip$ superconductor shows isotropic behavior for the supercurrent, while the p-wave superconductor shows anisotropic behavior for the supercurrent.Comment: Version 4. 18 pages, 9figures. New results of the anisotropic behavior for the supercurrent in p-wave model added. Accepted by PR