Heteroborospherene nanoclusters as high-performance nonlinear optical materials

Today, the design of new compounds with giant nonlinear optical responses is attracted to many researchers. Inspired by an interesting finding of a new class of heteroborospherenes which were formed by doping four carbon atoms in the B364- nanocluster (C4B32), we suggest the alkali metal-doped C4B32 (M@C4B32, M=Li, Na, and K) nanoclusters as high-performance nonlinear optical materials. Our results show that the alkali metal atoms have a considerable effect on the structural and electronic properties of the C4B32 nanocluster. We found that the doping alkali metal can remarkably decrease the HOMO-LUMO gap and significantly increases the first hyperpolarizability of the C4B32 nanocluster. Also, our results reveal that the first hyperpolarizability of the M@C4B32 nanoclusters can be progressively enhanced by increasing the atomic number of alkali metals. The effect of external electric fields on the nonlinear optical responses of the M@C4B32 has been systematically explored. We found that the first hyperpolarizability of the M@C4B32 compounds can be gradually increased by increasing the imposed external electric field from zero to the critical external electric field along the charge transfer direction (M→C4B32). Accordingly, this work presents an efficient strategy to improve the nonlinear optical responses of the heteroborospherenes.     

Coupling and exponential ergodicity for stochastic differential equations driven by Lévy processes

We present a novel idea for a coupling of solutions of stochastic differential equations driven by Lévy noise, inspired by some results from the optimal transportation theory. Then we use this coupling to obtain exponential contractivity of the semigroups associated with these solutions with respect to an appropriately chosen Kantorovich distance. As a corollary, we obtain exponential convergence rates in the total variation and standard $L^1$-Wasserstein distances.     

Log-likelihood maximization and response surface in reliability assessment

Nonlinear dynamics problems can generally be solved only in a numerical way. This prevents from a direct application of standard reliability methods. A technique which makes use of iterated response-surface analytical approximations of the system performance function was therefore proposed in view of reliability assessment. The limitation of this technique was of working in a standard normalized space, so that appropriate space transformations are preliminarly required.This paper shows how this response-surface iterative scheme can also be used in the original space of the random variables, provided a maximum log-likelihood constrained optimization problem is solved. Moreover, asymptotic theory also provides a better estimate of the probability of failure of the dynamical system against any assigned limit state.     

Eléments finis stochastiques en élasticité linéaireA stochastic finite element method in linear mechanics

The stochastic finite element method presented in this Note consists in representing in a probabilistic form the response of a linear mechanical system whose material properties and loading are random. Each input random variable is expanded into a Hermite polynomial series in standard normal random variables. The response (e.g., the nodal displacement vector) is expanded onto the so-called polynomial chaos. The coefficients of the expansion are obtained by a Galerkin-type method in the space of probability. To cite this article: B. Sudret et al., C. R. Mecanique 332 (2004).     

Transient response of a finite crack in an orthotropic strip under the in-plane shear impact

The transient response of a central crack in an orthotropic strip under the in-plane shear impact loading is studied by using the dual integral equation method proposed by Copson and Sih. The general formula for the shear stress intensity factor near the crack tip is derived. Numerical results of with in various cases are obtained by solving the second kind Fredholm integral equation and by performing the inverse Laplace transform.     

Stability of noisy nonlinear auto-parametric systems

The purpose of this work is to examine the stationary motion and stability properties of stationary motion of two degree-of-freedom noisy auto-parametric systems We shall use analytical techniques to extend the existing results to examine such multi-dimensional nonlinear systems with noise, and in particular additive white noise. We obtain an approximation for the top Lyapunov exponent, the exponential growth rate, of the response of the so-called single-mode stationary motion. We show analytically that the top Lyapunov exponent is positive, and for small values of noise intensity ɛ and dissipation ɛ² the exponent grows in proportion with ɛ^2/3.     

Non-Linear Self-Excited Random Vibrations and Stability of an SDOF System with Parametric Noises

Abstract. The paper presents the solution to the properties of stochastic response of a system with random parametric noises, which is prone to the loss of aerodynamical stability. The system is described by an equation of van der Pol type with the negative linear, and with the positive cubic dampings. The coefficients of the linear damping and of the stiffness include the multiplicative random perturbations, the external excitation being given as a sum of a deterministic function and of an additive perturbation. All three input random processes are supposed to be Gaussian and centered, with the non-zero mutual stochastic parameters, as it corresponds to the properties of real systems. The solution has been based on the method of stochastic linearisation and of the subsequent solution of the Fokker–Planck–Kolmogorov equation in the sense of the first and second stochastic moments for the transient and stationary states. There have been demonstrated several effects, which are typical for systems with parametric noises, differentiating them from the systems with constant coefficients. The principal attention has been devoted to the properties of the spectral density of the response, the character of which changes abruptly with the degree of non-linearity of the damping and of the level of random perturbations.Sommario. La presente memoria studia le proprietà della risposta stocastica di un sistema con eccitazione casuale parametrica, che tende alla perdita della stabilità aerodinamica. Il sistema è descritto mediante un'equazione del tipo di van der Pole con il termine lineare dello smorzamento negativo e il termine cubico positivo. Poichá l'eccitazione esterna è la somma di una funzione deterministica e di una perturbazione additiva, i coefficienti dello smorzamento lineare e della rigidezza comprendono le perturbazioni casuali moltiplicative. I tre processi stocastici di eccitazione sono assunti gaussiani e a media nulla con parametri stocastici incrociati diversi da zero, come si verifica per le proprietà dei sistemi reali. La soluzione è basata sul metodo della linearizzazione stocastica e della successiva soluzione dell'equazione di Fokker-Planck-Kolmogorov studiando i primi e i secondi momenti statistici per gli stati transitori e stazionari. Vengono mostrati diversi effetti, tipici dei sistemi con eccitazione parametrica, differenziandoli dai sistemi a coefficienti costanti. Particolare attenzione è rivolta alle proprietà della densità spettrale della risposta le cui caratteristiche cambiano bruscamente con il grado di non linearità dello smorzamento e del livello di casualità delle perturbazioni.     

频响函数综合法预测结构在水下的动特性

通过对一个结构模型在空气中和水下的动特性的研究，探讨了由结构在空气中的模态参数和水的附加质量预测结构在水下的模态参数的频响函数综合法，用以替代实体结构在水下的动特性试验。应用这种方法预测得到了结构在水下的模态参数并与结构的湿模态试验结果进行了对比。研究结果表明，对于所研究的梁形结构，不考虑水的阻尼，将水对结构的影响考虑成为附加质量，应用频响函数综合法预测结构在水下的模态参数是可行的     

Steady-shear viscosity and transient stress response for elasto-thixotropic fluids

A phenomenological model for dispersed systems which exhibit complex rheological behaviour such as shear and time-dependent viscosity, yield stress, and elasticity is proposed. The model extends the Quemeda model to describe the viscosity function with a structural parameter λ which varies according to different kinetic orders of particle aggregation and segregation. The transient stress response is obtained by solving an instantaneous Maxwell model with an assumed shear modulus functionG of the same form as the viscosity function η. Accuracy of the proposed model is verified experimentally with the results obtained for two oil (creosote)/water emulsions. The model that gives the best fit of experimental data appears to be the one with kinetic ordersn=m=2.