中国传统音乐“线性”现象及成因分析

由于中国的传统生产方式、儒家思想、音乐思维方式、乐器与乐人及其他艺术等多方面的影响,在中国音乐史上,众多音乐作品都是单旋律的,形成了一种"线性"现象,与西方音乐形成了鲜明的对比。

高校合并的非线性思路

线性与非线性本是数学名词,非线性是相对于线性而言。所谓线性就是符合简单的比例关系,叠加原理成立,量与量之间的关系用直角坐标系形象地表示出来时是一条直线。从物理现象来看,线性现象是在空间和时间中呈光滑和规则的运动。非线性就不受比例关系和叠加原理所囿,量与量相互作用产生新质,整体不等于部分之和。非线性现象是从规则运动向不规则运动的过渡和突变,非线性系统的响应与线性系统有着本质的不同。

On the Blowing-up Behaviours for Nonlirear Wave Equations

This paper deals with the initial-boundary value mixed problems for nonlinear wave equations. By introducing the 'blowing-up facts K(u,u_i)', We may discuss the blowing up behaviours of solutions in finite time to the mixed problems with respect to Neumann boundary and Dirichlet boundary for various nonlinear conditions and initial value conditions which usually meet.

Painleve Analysis and Determinant Solutions of a (3+1)-Dimensional Variable-Coefficient Kadomtsev-Petviashvili Equation in Wronskian and Grammian Form

In this paper, the investigation is focused on a （3＋1）-dimensional variable-coefficient Kadomtsev- Petviashvili （vcKP） equation, which can describe the realistic nonlinear phenomena in the fluid dynamics and plasma in three spatial dimensions. In order to study the integrability property of such an equation, the Painlevé analysis is performed on it. And then, based on the truncated Painlevé expansion, the bilinear form of the （3＋1）-dimensionaJ vcKP equation is obtained under certain coefficients constraint, and its solution in the Wronskian determinant form is constructed and verified by virtue of the Wronskian technique. Besides the Wronskian determinant solution, it is shown that the （3＋1）-dimensional vcKP equation also possesses a solution in the form of the Grammian determinant.

Two-Soliton Solutions and Interactions for the Generalized Complex Coupled Kortweg-de Vries Equations

Kortweg-de Vries （KdV）-typed equations have been used to describe certain nonlinear phenomena in fluids and plasmas. Generalized complex coupled KdV （GCCKdV） equations are investigated in this paper. Through the dependent variable transformations and symbolic computation, GCCKdV equations are transformed into their bilinear forms, based on which the one- and two-soliton solutions are obtained. Through the interactions of two solitons, the regular elastic collision are shown. When the wave numbers are complex, three kinds of solitonie collisions are presented： （i） two solitons merge and separate from each other periodically; （ii） two solitons exhibit the attraction and repulsion nearly twice, and finally separate from each other after such type of interaction; （iii） two solitons are ftuctuant in the central region of the collision. Propagation features of solitons are investigated with the effects of the coefficients in the GCCKdV equations considered. Velocity of soliton increase with the a increasing. Amplitude of v increase with the a increasing and decrease with the β increasing.

A new scheme of implementing all-optical logic systems exploiting material nonlinearity and polarization based encoding technique

In this letter,the authors propose a new concept of implementing all-optical logic gates by representing the logic states with polarization of an optical signal .As the state of polarization of the light signal is very much suitable for encoding and detecting the bits of data of a digital signal in communication,the scheme may extend some wide applications in all-optical parallel computation and information processing.

Traditional El Nio and El Ni o Modoki Revisited:Is El Nio Modoki Linearly Independent of Traditional El Nio?

The present study revisited the first two leading modes of tropical Pacific sea surface temperature anomalies （SSTA） during the period of 1979-2008. It is suggested that the so-called El Nino Modoki, which is captured by the second mode, exists objectively and exhibits obvious differences from traditional El Nifio, which is captured by the first mode, in terms of its spatial characteristics. Furthermore, the authors found that El Nino Modoki is linearly independent of traditional El Nino; hence, it cannot be described as part of the traditional El Nino evolution, and vice versa.

Financial Rogue Waves

We analytically give the financial rogue waves in the nonlinear option pricing model due to Ivancevic,which is nonlinear wave alternative of the Black-Scholes model.These rogue wave solutions may be used to describe thepossible physical mechanisms for rogue wave phenomenon in financial markets and related fields.

Free vibration of vibrating device coupling two pendulums using multiple time scales method

A model of vibrating device coupling two pendulums (VDP) which is highly nonlinear was put forward to conduct vibration analysis. Based on energy analysis, dynamic equations with cubic nonlinearities were established using Lagrange's equation. In order to obtain approximate solution, multiple time scales method, one of perturbation technique, was applied. Cases of non-resonant and 1:1:2:2 internal resonant were discussed. In the non-resonant case, the validity of multiple time scales method is confirmed, comparing numerical results derived from fourth order Runge-Kutta method with analytical results derived from first order approximate expression. In the 1:1:2:2 internal resonant case, modal amplitudes of Aa1 and Ab2 increase, respectively, from 0.38 to 0.63 and from 0.19 to 0.32, while the corresponding frequencies have an increase of almost 1.6 times with changes of initial conditions, indicating the existence of typical nonlinear phenomenon. In addition, the chaotic motion is found under this condition.

Novel measurement scheme of peak separation of side-hole fiber grating

There are two peaks of different polarizations in the reflection spectrum of the side-hole fiber grating and their separation interval has a linear variation along with the pressure changing while it is insensitive to the temperature.We have proposed a novel measurement scheme based on polarization detection.The detection of peak separation is achieved by measuring the two peaks’ center wavelengths separately with all polarization maintaining fiber system.The side-hole fiber grating pressure sensing within the range of 0～3.5 MPa is realized successfully with the new scheme.

Phenomenon of Resonance in a Two-Mode Laser with an Input Additive Signal

Exact formulas for the power spectrum and signal-to-noise ratio (SNR) with periodic additive signal arecalculated in the linear system.Then the phenomenon of resonance is studied in detail.We show that resonancepeak and suppressed valley exist in the curves of the SNR versus the coefficient of self-saturation, the net gain and thecross-coupling coefficient of the laser system.

Quasilinear Hyperbolic Conservation Laws with Relaxation

In this paper, we investigate the relaxation phenomenon for quasilinear hyperbolic conservation laws, and obtain global smooth solutions and the life span of classical solutions to its Cauchy problem. These results shows that the relaxation admits the effects of dissipation.

What is the sound of fear？ Behavioral responses of white-crowned sparrows Zonotrichia leucophrys to synthesized nonlinear acoustic phenomena

Fear and anxiety may be adaptive responses to life-threatening situations, and animals may communicate fear to others vocally. A fundamental understanding of fear inducing sounds is important for both wildlife conservation and management because it helps us understand how to design repellents and also how （and why） animals may be negatively impacted by anthropogenic sounds. Nonlinear phenomena--sounds produced by the desynchronization of vibrations in a sound production system-are commonly found in stress-induced animal vocalizations, such as in alarm calls, mobbing calls, and fear screams. There are several functional hypotheses for these nonlinear phenomena. One specific hypothesis is the unpredictability hypothesis, which suggests that because nonlinear phenomena are more variable and somewhat unpredictable, animals are less likely to habituate to them. Animals should, therefore, have a prolonged response to sounds with nonlinear phenomena than sounds without them. Most of the studies involving nonlinear phenomena have used mammalian subjects and conspecific stimuli. Our study fo- cused on white-crowned sparrows （Zonotrichia leucophrys ssp. oriantha） and used synthesized acoustic stimuli to investigate behavioral responses to stimuli with and without nonlinear phenomena. We predicted that birds would be less relaxed after hearing a stimulus with a nonlinear component. We calculated the difference from baseline of proportion of time spent in relaxed behaviors and performed pair-wise comparisons between a pure tone control stimulus and each of three experimental stimuli, including a frequency jump up, a frequency jump down, and white noise. These comparisons showed that in the 30q50 s after the playback experiment, birds were significantly less relaxed after hearing noise or an abrupt frequency jump down an octave but not an abrupt frequency jump up an octave or a pure tone. Nonlinear phenomena, therefore, may be generally arousing to animals and may explain why these acoustic properties are commonly found in animal signals associated with fear [Current Zoology 60 （4）： 534-541, 2014].

Dynamical Entanglement of Vibrations in Integrable Dimer and Small Molecules

By means of the reduced-density linear entropy, we investigate the properties of dynamical entanglement of vibrations in integrable dimer and realistic small molecules which are initially in the two-mode squeezed vacuum state. It is found that the entropy of the integrable dimer is periodic for weak coupling strength cl and small squeezing parameter r, and there exists a beat phenomenon for strong el and large r. Moreover, the entropy of the small molecules is quasi-periodic for small r, ＆nd the begt phenomenon occurs in the entropy evolution of the two molecules C2D2 and S02 for large r. Our results might be used for molecular quantum computing based on vibrational states.

Study on the Cylindrical Liquid Nanojet Break-up Phenomenon

In this paper the liquid argon nanojet break-up phenomenon was studied using the molecular dynamics method. The effects of temperature, nozzle diameter and body force on the nanojet break-up length and time were simu- lated. Meanwhile, the particle size, wave length and the frequency of the disturbance were compared with the re- suits of linear stability analysis. The results showed that even though the fluid becomes discontinuous, the tradi- tional linear stability analysis can be used to make a rough calculation of the nanojet break-up.