On Constructing the Analytical Solutions for Localizations in a Slender Cylinder Composed of an Incompressible Hyperelastic Material

In this paper, we study the localization phenomena in a slender cylinder composed of an incompressible hyperelastic material subjected to axial tension. We aim to construct the analytical solutions based on a three-dimensional setting and use the analytical results to describe the key features observed in the experiments by others. Using a novel approach of coupled series-asymptotic expansions, we derive the normal form equation of the original governing nonlinear partial differential equations. By writing the normal form equation into a first-order dynamical system and with the help of the phase plane, we manage to solve two boundary-value problems analytically. The explicit solution expressions (in terms of integrals) are obtained. By analyzing the solutions, we find that the width of the localization zone depends on the material parameters but remains almost unchanged for the same material in the post-peak region. Also, it is found that when the radius-length ratio is relatively small there is a snap-back phenomenon. These results are well in agreement with the experimental observations. Through an energy analysis, we also deduce the preferred configuration and give a prediction when a snap-through can happen. Finally, based on the maximum-energy-distortion theory, an analytical criterion for the onset of material failure is provided.Comment: 27 pages 10 figure

Photocatalytic hydrogen evolution over nickel cobalt bimetallic phosphate anchored graphitic carbon nitrides by regulation of the d-band electronic structure

Non-precious metal co-catalysts with high activity and stability are extremely desirable for economically viable photocatalytic molecular hydrogen (H₂) evolution. Herein, nickel cobalt phosphate (NiCo–Pi) was introduced into graphitic carbon nitride layers (g-C₃N₄) via a sonication-assisted ion intercalation method as a substitute for noble metal co-catalysts. Under visible light irradiation, NiCo–Pi/g-C₃N₄ (Ni/Co molar ratio of 4 : 5) exhibited the highest photocatalytic activity (ca. 10 184 μmol h⁻¹ g⁻¹) and stability for H₂ evolution. Synchrotron radiation X-ray absorption spectroscopy (XAS) indicated that NiCo–Pi is closely bound to g-C₃N₄ via covalent binding, which accelerates electron transport. Moreover, the unoccupied d-orbital in NiCo–Pi causes the surface to strongly adsorb atomic hydrogen (*H). Theoretically, density functional theory (DFT) calculations demonstrated that the d-band center position of NiCo–Pi is relocated upon adjusting the Ni/Co molar ratio, which changes the adsorption energy of NiCo–Pi toward intermediate state *H. This work provides new insights for exploring the role of the bimetallic composition in non-noble co-catalysts for highly efficient H₂ evolution

Photocatalytic hydrogen evolution over nickel cobalt bimetallic phosphate anchored graphitic carbon nitrides by regulation of the d-band electronic structure

Non-precious metal co-catalysts with high activity and stability are extremely desirable for economically viable photocatalytic molecular hydrogen (H₂) evolution. Herein, nickel cobalt phosphate (NiCo–Pi) was introduced into graphitic carbon nitride layers (g-C₃N₄) via a sonication-assisted ion intercalation method as a substitute for noble metal co-catalysts. Under visible light irradiation, NiCo–Pi/g-C₃N₄ (Ni/Co molar ratio of 4 : 5) exhibited the highest photocatalytic activity (ca. 10 184 μmol h⁻¹ g⁻¹) and stability for H₂ evolution. Synchrotron radiation X-ray absorption spectroscopy (XAS) indicated that NiCo–Pi is closely bound to g-C₃N₄ via covalent binding, which accelerates electron transport. Moreover, the unoccupied d-orbital in NiCo–Pi causes the surface to strongly adsorb atomic hydrogen (*H). Theoretically, density functional theory (DFT) calculations demonstrated that the d-band center position of NiCo–Pi is relocated upon adjusting the Ni/Co molar ratio, which changes the adsorption energy of NiCo–Pi toward intermediate state *H. This work provides new insights for exploring the role of the bimetallic composition in non-noble co-catalysts for highly efficient H₂ evolution

Canonical explicit B\"{a}cklund transformations with spectrality for constrained flows of soliton hierarchies

It is shown that explicit B\"{a}cklund transformations (BTs) for the high-order constrained flows of soliton hierarchy can be constructed via their Darboux transformations and Lax representation, and these BTs are canonical transformations including B\"{a}cklund parameter $\eta$ and possess a spectrality property with respect to $\eta$ and the 'conjugated' variable $\mu$ for which the pair $(\eta, \mu)$ lies on the spectral curve. As model we present the canonical explicit BTs with the spectrality for high-order constrained flows of the Kaup-Newell hierarchy and the KdV hierarchy.Comment: 21 pages, Latex, to be published in "PHYSICA A

Constructing N-soliton solution for the mKdV equation through constrained flows

Based on the factorization of soliton equations into two commuting integrable x- and t-constrained flows, we derive N-soliton solutions for mKdV equation via its x- and t-constrained flows. It shows that soliton solution for soliton equations can be constructed directly from the constrained flows.Comment: 10 pages, Latex, to be published in "J. Phys. A: Math. Gen.

B\"{a}cklund transformations for high-order constrained flows of the AKNS hierarchy: canonicity and spectrality property

New infinite number of one- and two-point B\"{a}cklund transformations (BTs) with explicit expressions are constructed for the high-order constrained flows of the AKNS hierarchy. It is shown that these BTs are canonical transformations including B\"{a}cklund parameter $\eta$ and a spectrality property holds with respect to $\eta$ and the 'conjugated' variable $\mu$ for which the point $(\eta, \mu)$ belongs to the spectral curve. Also the formulas of m-times repeated Darboux transformations for the high-order constrained flows of the AKNS hierarchy are presented.Comment: 21 pages, Latex, to be published in J. Phys.

Applications of Nanomaterials in Electrochemical Enzyme Biosensors

A biosensor is defined as a kind of analytical device incorporating a biological material, a biologically derived material or a biomimic intimately associated with or integrated within a physicochemical transducer or transducing microsystem. Electrochemical biosensors incorporating enzymes with nanomaterials, which combine the recognition and catalytic properties of enzymes with the electronic properties of various nanomaterials, are new materials with synergistic properties originating from the components of the hybrid composites. Therefore, these systems have excellent prospects for interfacing biological recognition events through electronic signal transduction so as to design a new generation of bioelectronic devices with high sensitivity and stability. In this review, we describe approaches that involve nanomaterials in direct electrochemistry of redox proteins, especially our work on biosensor design immobilizing glucose oxidase (GOD), horseradish peroxidase (HRP), cytochrome P450 (CYP2B6), hemoglobin (Hb), glutamate dehydrogenase (GDH) and lactate dehydrogenase (LDH). The topics of the present review are the different functions of nanomaterials based on modification of electrode materials, as well as applications of electrochemical enzyme biosensors

Search for the decay J/ψ→γ+invisibleJ/\psi\to\gamma + \rm {invisible}

We search for $J/\psi$ radiative decays into a weakly interacting neutral particle, namely an invisible particle, using the $J/\psi$ produced through the process $\psi(3686)\to\pi^+\pi^-J/\psi$ in a data sample of $(448.1\pm2.9)\times 10^6$ $\psi(3686)$ decays collected by the BESIII detector at BEPCII. No significant signal is observed. Using a modified frequentist method, upper limits on the branching fractions are set under different assumptions of invisible particle masses up to 1.2 $\mathrm{\ Ge\kern -0.1em V}/c^2$. The upper limit corresponding to an invisible particle with zero mass is 7.0$\times 10^{-7}$ at the 90\% confidence level

First observations of hc→h_c \to hadrons

Based on $(4.48 \pm 0.03) \times 10^{8}$ $\psi(3686)$ events collected with the BESIII detector, five $h_c$ hadronic decays are searched for via process $\psi(3686) \to \pi^0 h_c$. Three of them, $h_c \to p \bar{p} \pi^+ \pi^-$, $\pi^+ \pi^- \pi^0$, and $2(\pi^+ \pi^-) \pi^0$ are observed for the first time, with statistical significances of 7.4$\sigma$, $4.9\sigma$, and 9.1$\sigma$, and branching fractions of $(2.89\pm0.32\pm0.55)\times10^{-3}$, $(1.60\pm0.40\pm0.32)\times10^{-3}$, and $(7.44\pm0.94\pm1.56)\times10^{-3}$, respectively, where the first uncertainties are statistical and the second systematic. No significant signal is observed for the other two decay modes, and the corresponding upper limits of the branching fractions are determined to be $B(h_c \to 3(\pi^+ \pi^-) \pi^0)<8.7\times10^{-3}$ and $B(h_c \to K^+ K^- \pi^+ \pi^-)<5.8\times10^{-4}$ at 90% confidence level.Comment: 17 pages, 16 figure