Stability of forced periodic response in third order non-linear systems

Conditions for the stability of forced periodic response in third order non-linear systems are obtained after linearization. These conditions are consistent with results obtained by other methods.     

Lower bound on forcing amplitude for stability of forced oscillations in a third order non-linear system

An example of a third order non-linear system is given which exhibits the property that stable symmetric forced oscillations exist only if the forcing amplitude is greater than a critical value.     

Mathieu stability analysis of non-linear third-order weakly forced systems

A Mathieu type of stability analysis for evaluating the stability of singular points having a periodic solution is presented here in a more complete form.     

On the third order elastic constants of AgCl-AgBr mixed system

Lowdin's many body effect is accounted to explain the violation of Cauchy's relation (C₁₂=C₄₄) in silver halides. Lundqvists potential model with many body effect has been used to evaluate the third order elastic constants of AgCl and AgBr. A modified Lundqvist potential model is used to calculate the third order elastic constants for the simple AgCl- AgBr mixed system with varying concentration of AgCl and AgBr.     

On wave solutions of a weakly nonlinear and weakly dispersive two-mode wave system

Abstract

In this paper, we introduce and study rigorously a Hamiltonian structure and soliton solutions for a weakly dissipative and weakly nonlinear medium that governs two Korteweg–de vries (KdV) wave modes. The bounded solution and traveling wave solution such as cnoidal wave and solitary wave are obtained. Subsequently, the equation is numerically solved by Fourier spectral method for its two-soliton solution. These solutions may be useful to explain the nonlinear dynamics of waves for an equation supporting multi-mode weakly dispersive and nonlinear wave medium. In addition, we give an explicit explanation of the mathematics behind the soliton phenomenon for a better understanding of the equation.     

Comments on “multiple time scaling for analysis of third order non-linear differential equations”

In order to better estimate how and to what extent people are affected by exposure to environmental noise, an attempt must be made to calculate first the size of the entire population exposed to certain levels of noise and, second, groups within the population which are particularly sensitive to noise. Such a study has been started in the Federal Republic of Germany. It has been estimated that about 14 million people are exposed to sound levels of roughly 62 dB(A) and about 2 million to levels of roughly 70 dB(A). Nothing is yet known about the existence or size of sensitive groups within these populations, however, and the following report lists areas needing research in terms of this problem.     

关于岩石三阶弹性常数的超声测量方法

油气储层岩石的三阶弹性常数反映了该岩石的速度应力敏感性,是利用声波测井或地震资料进行原位地应力反演的基本参数。本文阐述了利用声弹性理论在实验室测量岩石三阶弹性常数的原理与方法,并给出了部分实验结果。这些参数将为研究声波在预应力声场中传播规律的提供基础数据,同时也为定量分析利用交叉偶极声波测井评价地应力的精度提供了依据。不同岩石的三阶弹性常数较大差异表明,通过速度各向异性进行应力反演时必须考虑岩石本身非线性的差异。     

On the chiral effective meson-baryon Lagrangian at third order⋆

We show that the recently constructed complete and “minimal” third-order meson-baryon effective chiral Lagrangian can be further reduced from 84 to 78 independent operators.     

On non-linear oscillations with slowly varying system parameters

The paper deals with an approximate analysis of non-linear oscillation problems with slowly varying system parameters. From the differential equations for amplitude and phase, set up by the method of variation of parameters, the approximate solutions are obtained by using the generalized averaging method of Sinha and Srinivasan based on ultraspherical polynomial expansions. The Bogoliubov-Mitropolsky results are given by a particular set of these polynomials. Problems of a single degree of freedom system as well as monofrequency oscillations in systems with multiple degrees of freedom are considered. The approach has been illustrated by an example and the results are compared with the numerical solutions. A close agreement is found.     

Vertically forced surface wave in weakly viscous fluids bounded in a circular cylindrical vessel

Two-time scale perturbation expansions were developed in weakly viscous fluids to investigate surface wave motions by linearizing the Navier－Stokes equation in a circular cylindrical vessel which is subject to a vertical oscillation. The fluid field was divided into an outer potential flow region and an inner boundary layer region. A linear amplitude equation of slowly varying complex amplitude, which incorporates a damping term and external excitation, was derived for the weakly viscid fluids. The condition for the appearance of stable surface waves was obtained and the critical curve was determined. In addition, an analytical expression for the damping coefficient was determined and the relationship between damping and other related parameters (such as viscosity, forced amplitude, forced frequency and the depth of fluid, etc.) was presented. Finally, the influence both of the surface tension and the weak viscosity on the mode formation was described by comparing theoretical and experimental results. The results show that when the forcing frequency is low, the viscosity of the fluid is prominent for the mode selection. However, when the forcing frequency is high, the surface tension of the fluid is prominent.