Theoretical Investigation on the Second-order Nonlinear Optical Properties of Chiral Amino Acid Zinc（Ⅱ） Porphyrins

Static second-order nonlinear optical effects of amino acid zinc(Ⅱ) porphyrins 1, 2,3 and 4 were calculated by the TDHF/PM3 method based on the molecular structures optim.zed at the semiempirical PM3 quantum chemistry level, showing due to the cancellation of symmetric center, these amino acid zinc(H) porphyrins exhibit second order nonlinear optical response. The analysis of β components indicated that these amino acid zinc(Ⅱ) porphyrins are of multipolarizabilities, and they may be ascribed as the “mixture” of octupolar and dipoar molecules with ||βJ=3||/||βJ=1||≈5. It is found that there are no significant differences between the static β values of non-chiral and chiral amino acid zinc(Ⅱ) porphyrins. However, the βxyz component, which is quite important to quadratic macroscopic X^(2) susceptibility of chiral material, is increased significantly with the increase of side chain group of amino acids.     

Adaptive approach for nonlinear sensitivity analysis of reaction kinetics

We present a unified approach for linear and nonlinear sensitivity analysis for models of reaction kinetics that are stated in terms of systems of ordinary differential equations (ODEs). The approach is based on the reformulation of the ODE problem as a density transport problem described by a Fokker-Planck equation. The resulting multidimensional partial differential equation is herein solved by extending the TRAIL algorithm originally introduced by Horenko and Weiser in the context of molecular dynamics (J. Comp. Chem. 2003, 24, 1921) and discussed it in comparison with Monte Carlo techniques. The extended TRAIL approach is fully adaptive and easily allows to study the influence of nonlinear dynamical effects. We illustrate the scheme in application to an enzyme-substrate model problem for sensitivity analysis w.r.t. to initial concentrations and parameter values.     

Preparation and Characterization of N-4-Nitrophenyl-L-prolinol Nanocrystals in Sol-Gel Matrices

Organic nanocrystals of N-4-nitrophenyl-l-prolinol (NPP) have been grown in sol-gel matrices prepared from silicon alkoxide precursors. Our process is based on the control of the nucleation and growth kinetics of the dye in the pores of dense gels. Nanocomposites gel-glasses are obtained with a high optical quality due to the small size of the nanocrystals (10-20 nm). Differential scanning calorimetry experiments evidenced clearly the melting point of NPP nanocrystals, which is registered 51°C above that of NPP powder. Micro-Raman and solid state NMR spectroscopies allowed us to demonstrate that our nanocrystallization process does not chemically modify NPP molecules. We specified also the nature of interactions existing between the NPP nanocrystals and the xerogels. These strong interactions, which explain the important increase of the melting point of the nanocrystals in comparison to the NPP powder, are hydrogen bonds between nitro groups of NPP and uncondensed silanol functions of the silicate network.     

Progress on phthalocyanine-conjugated Ag and Au nanoparticles: Synthesis,characterization, and photo-physicochemical properties

Phthalocyanine (Pc) complexes are an important class of dyes with numerous (e.g., biological, photophysical, and analytical) applications. Among the methods used to improve the properties of these complexes, one should mention the introduction of different substituents, variation of the central metal ion, ligand exchange, and conjugation to nanomaterials (e.g., carbon-based nanomaterials and metal nanoparticles (NPs)). This work briefly reviews Pc complex conjugation to Ag and Au NPs, highlights the different NP shapes, and discusses the diversity of conjugation approaches. Moreover, the use of UV–Vis spectroscopy, powder X-ray diffraction, X-ray photoelectron spectroscopy, transmission electron microscopy, atomic force microscopy, dynamic light scattering and Fourier transform infrared spectroscopy to characterize Pc-NP hybrids is summarized. The effect of conjugation on Pc photo-physicochemical properties (fluorescence, singlet oxygen generation, triplet state formation, and optical limiting behavior) is discussed, and future perspectives for the synthesis and applications of new hybrids are provided.     

Second-order nonlinear optical properties of side-chain liquid crystalline polymers studied by second harmonic generation from thin films

The two independent elements of the second-order nonlinear optical susceptibility tensor of a range of contact poled, donor–acceptor substitued side-chain polymers are reported. The susceptibilities were measured by second harmonic generation from thin films, typically less than 0.5 μm thick, at a fundamental wavelength of 1064 nm. The largest value was χ = 2.64 pm/V which is three times greater than the χ value of KDP and was measured in a nitrobenzylidene side chain, polyhydroxystyrene polymer with an eleven unit alkyl chain spacer attaching the side group to the backbone. Typical susceptibility values obtained were χ～0.3 pm/V and X⁽²⁾₃₃～1 pm/V. The coherence lengths of the materials, which lay in the range 4–12 μm, were measured at 1064 nm by the maker fringe technique using thick, wedge-shaped samples.     

Nonlinear Optical Properties of Tri—nuclear Transition Metal Clusters M—（μ—S）s—M′（M=Mo,W;M′=Cu,Ag,Au）

The static polarizabilities and the second-order hyperpolarizabilities of a series of tri-nuclear metal cluster models MS4(M′PPh3)2(M′PPh3)(M=Mo,W;M′=Cu,Ag,Au)have been calculated within the first-principle theoretical framework. The model clusters have two fragments of rhombic units and it is the charge ransfer from one of these moieties to the other that is responsible for nonlinear optical property. This kind of electronic delocaization, differentiated from that of planar π-system, is very interesting and is worthy for further investigation.     

Doped Sol-Gel Films for Silica-on-Silicon Photonic Components

Further expansion of optical communication systems depends strongly on the development of cheap component technologies for functions such as switching, demultiplexing and amplification. Silica-on-silicon is increasingly recognised as the best approach to low cost integrated optics for such applications, but so far the functionality is limited. The purpose of NODES, a basic research collaboration sponsored by the European Union under the programme ESPRIT, has been to examine the application of sol-gel to a highly functional silica-on-silicon technology. In particular, the project has investigated film processing and characterisation, rare-earth doping for amplification, and semiconductor nanocrystallite doping for nonlinear functions. This paper presents the background and context to this work, summarises the technical results obtained, and discusses requirements and challenges for successful application of sol-gel in photonics.     

The Discrete Approximation of Continuous-state Nonlinear Branching Processes in Lévy Random Environments北大核心CSCD

In this paper, we establish the discrete approximation of continuous-state nonlinear branching processes in Lévy random environments by using tightness and convergence sequence in infinite dimensional product space via stochastic differential equations. Taking α-stable branching as an example, the conditions which are given to discretize continuous-state nonlinear branching processes in Lévy random environments are verified. © 2022 Chinese Academy of Sciences. All rights reserved.     

带五次项的非线性Schrödinger方程的守恒差分格式

本文研究带有五次项的非线性Schrödinger方程初边值问题的有限差分法,其中方程中二阶偏导数项的系数、五次项的系数及初值满足下面的条件（1.6）.针对此问题,我们研究了一个守恒差分格式,在条件（1.6）下,差分解的$L^{\infty}$模先验估计被得到.在此基础上,我们得到了差分解最优$L^2$模的误差估计.     

Effects of Cone Angles on Nonlinear Vibration Responses of Functionally Graded Shells北大核心CSCD

The nonlinear vibration responses of functionally graded materials (FGMs) shells with different cone angles under external loads were studied. Firstly, the Voigt model was employed to describe the physical properties along the thickness direction of FGMs conical shells. Then, the motion equations were derived based on the 1st-order shear deformation theory, the von Kármán geometric nonlinearity and Hamilton’s principle. Next, the Galerkin method was applied to discretize the motion equations and the governing equations were simplified into a 1DOF nonlinear vibration differential equation under Volmir’s assumption. Finally, the nonlinear motion equations were solved with the harmonic balance method and the Runge-Kutta method, and the amplitude frequency response characteristic curves of the FGMs conical shells were obtained. The effects of different material distribution functions and different ceramic volume fraction exponents on the amplitude frequency response curves of conical shells were discussed. The bifurcation diagrams of conical shells with different cone angles, as well as time process diagrams and phase diagrams for different excitation amplitudes, were described. The motion characteristics were characterized by Poincaré maps. The results show that, the FGMs conical shells present the nonlinear characteristics of hardening springs. The chaotic motions of the FGMs conical shells are restrained and not prone to motion instability with the increase of the cone angle. The FGMs conical shell present a process from the periodic motion to the multi-periodic motion and then to chaos with the increase of the excitation amplitude. © 2022 Editorial Office of Applied Mathematics and Mechanics. All rights reserved.