The Riemann–Hilbert problem to coupled nonlinear Schrödinger equation: Long-time dynamics on the half-line

We derive the long-time asymptotics for the solution of initial-boundary value problem of coupled nonlinear Schrödinger equation whose Lax pair involves 3 × 3 matrix in present paper. Based on a nonlinear steepest descent analysis of an associated 3 × 3 matrix Riemann–Hilbert problem, we can give the precise asymptotic formulas for the solution of the coupled nonlinear Schrödinger equation on the half-line.     

Test of the Duh-Haymet-Henderson theory for mixtures: cavity correlation functions and excess volumes

The accuracy of the Duh-Haymet-Henderson (DHH) integral equation theory for predicting the cavity correlation functions of mixtures has been tested by comparison with molecular simulations. We have compared the cavity correlation functions, internal energies, and pressures computed for Lennard-Jones model mixtures of Ar/Kr, Ar/Ne, and Ar/Xe with these same quantities computed from the DHH theory and also, for reference, the Percus-Yevick (PY) integral equation theory. We found that DHH gave much better accuracy than PY at high densities. At low densities DHH and PY give essentially identical predictions. We have computed excess volumes for Ar/Kr mixtures at two pressures (10 and 20?MPa) at 132.32?K, for which experimentally derived data are available. The DHH theory predicts the correct trends and is quantitatively more accurate than the PY theory for predicting the excess volumes. We have tested the local optimality of the DHH theory for pure fluids by adding two adjustable parameters to the DHH bridge function expression to see if it is possible to improve the DHH predictions of the cavity correlation function empirically, holding the form of the bridge function constant. We found that no single set of adjustable parameter values could improve the accuracy of DHH over multiple different isotherms. Furthermore, perturbing DHH leads to a decrease in accuracy of the predictions of both the pressure and energy, although small improvements in the cavity correlation functions were achieved. Thus, the DHH theory is locally optimal, given the form of the bridge function.     

Structures,microstructures, physical and chemical properties of different rice grains

Herein, we demonstrated a well-rounded exploration of the universal structures, microstructures and physical properties of different rice grains. We show that these rice grains are nanocrystalline in nature, have the standard pattern of type A rice crystalline, and can be attributed to the hexagonal crystal structure with space group of P6. These rice grains have uneven surfaces, clusters of the granules, or schistose structure. Carbon, nitrogen and oxygen elements are presented in the rice grains. No significant difference is observed in FTIR spectra in these rice grains, indicating the fundamental chemical structures of these rice grains are analogical. Their microstructural and physical properties were investigated in detail. Moreover, chemical properties (e.g. thermal stability) of the rice grains were explored. This research provides an in-depth understanding on the physical and structural properties on the atomic and molecular level, as well as guidance for food and industry applications.     

Experimental research on distributed fiber sensor for sliding damage monitoring

A distributed optical fiber sensor (DOFS) with the principle of microbend loss has been developed for concrete or rock-sliding damage measurement. The combination of multiple microbend sensors can form a sensor array for distributed sensing application in monitoring local slippage or deformation along the rock mass of the high slope, and the optical time-domain reflectometry (OTDR) can be conveniently used for interrogation of each sensor point. The sensor sensitivity can be obtained at a specific range according to the requirement of the model test condition. Connected with multiplexed sensing processing schemes, its sliding range of dynamic sensing response reached 0–3.6 mm and semi-empirical formula was fitted according to data from model tests. The DOFS array may find a potential application in real-time monitoring and damage detection of large and critical slope engineering structures.     

Nonlinear optical switching matrix

We show that nonlinear directional couplers with variable coupling coefficients can be used to compose a special kind of switching matrix. The switching matrix can be controlled by the signal itself or by a strong pump. Light routing is realized by adjustment of the power of the signal or the pump. Because light routing is based on the optical Kerr effect, ultrafast routing is possible.     

Meyer-K(o)nig-Zeller 算子加权逼近的收敛阶

利用加权Ditzin-Totik 光滑模ω2φλ(f;t)w,借助Peetre K-泛函研究了Meyer-K(o)nig-Zeller算子,给出其特征刻画.     

Self-assembly of silanated poly(ethylene glycol) on silicon and glass surfaces for improved haemocompatibility

Surface immobilization of poly(ethylene glycol) (PEG) is an effective method to produce a material surface with protein repulsive property. This property could be made permanent by using covalent grafting of the PEG molecules onto material surfaces. In this study, self-assembled monolayers (SAMs) of PEG on silicon-containing materials (silicon chip and glassplate) were obtained through a one-step coating procedure of one kind of silanated PEG molecules made through the reaction between monomethoxy PEG and 3-isocyanatopropyltriethoxysilane. Atomic force microscopy (AFM) and water static contact angle measurement were employed to investigate the surface topography and wettability of the PEGylated material surfaces. The changes in the topography and the water contact angle of the surfaces with time of incubation in PBS solution were also measured. The results revealed that stable and uniform self-assembled monolayers of PEG could be formed on silicon or glass surfaces by simply soaking the substrates in the solution of silanated PEGs. The covalent coupling of PEGs to the substrates was also confirmed. In order to evaluate the stability of the SAMs, blood compatibility of the modified glassplate surface was evaluated by measuring full blood activated partial thromboplastin time (APTT), prothrombin time (PT), and thrombin time (TT), as well as by scanning electron microscopy (SEM) analysis of the appearance of adherence and denaturation of blood platelets onto the glassplate. The silanated PEGs were shown to have good effect on the protein-repulsion as well as haemocompatibility of the substrates.     

Hochschild (co)homology of Yoneda algebras of reconstruction algebras of type A 1

The reconstruction algebra is a generalization of the preprojective algebra, and plays important roles in algebraic geometry and commutative algebra. We consider the homological property of this class of algebras by calculating the Hochschild homology and Hochschild cohomology. Let Λ _t be the Yoneda algebra of a reconstruction algebra of type A ₁ over a field k. In this paper, a minimal projective bimodule resolution of Λ _t is constructed, and the k-dimensions of all Hochschild homology and cohomology groups of Λ _t are calculated explicitly.     

Effect of spike-timing-dependent plasticity on coherence resonance and synchronization transitions by time delay in adaptive neuronal networks

In this paper, we numerically study how time delay induces multiple coherence resonance (MCR) and synchronization transitions (ST) in adaptive Hodgkin-Huxley neuronal networks with spike-timing dependent plasticity (STDP). It is found that MCR induced by time delay STDP can be either enhanced or suppressed as the adjusting rate A_p of STDP changes, and ST by time delay varies with the increase of A_p, and there is optimal A_p by which the ST becomes strongest. It is also found that there are optimal network randomness and network size by which ST by time delay becomes strongest, and when A_p increases, the optimal network randomness and optimal network size increase and related ST is enhanced. These results show that STDP can either enhance or suppress MCR and optimal STDP can enhance ST induced by time delay in the adaptive neuronal networks. These findings provide a new insight into STDP’s role for the information processing and transmission in neural systems.     

A diffractive study of optical parametric interactions in nonlinear photonic crystals

With the nonlinear diffraction concept, we present a diffractive study of optical parametric interactions in nonlinear photonic crystals. The nonlinear diffraction concept enables the design of complicated nonlinear photonic crystal structures in an intuitive way. We show that there are two basic linear sequences, the anti-stacking and the para-stacking sequences, existing in a one-dimensional structure; and we present the realization of multiple phase-matching resonances in the combination of the two basic sequences. The parameters affecting the structure factor of a two-dimensional nonlinear photonic crystal are investigated, which indicate that not only the Ewald construction but also the relative domain size determines two-dimensional nonlinear diffractions.