Traveling waves in trimer granular lattice I: Bifurcation structure of traveling waves in the unit-cell model

Present paper is the first one in the series devoted to the dynamics of traveling waves emerging in the uncompressed, tri-atomic granular crystals. This work is primarily concerned with the dynamics of one-dimensional periodic granular trimer (tri-atomic) chains in the state of acoustic vacuum. Each unit cell consists of three spherical particles of different masses subject to periodic boundary conditions. Hertzian interaction law governs the mutual interaction of these particles. Under the assumption of zero pre-compression, this interaction is modeled as purely nonlinear, which means the absence of linear force component. The dynamics of such chains is governed by the two system parameters that scale the mass ratios between the particles of the unit cell. Such a system supports two different classes of periodic solutions namely the traveling and standing waves. The primary objective of the present study is the numerical analysis of the bifurcation structure of these solutions with emphasis on the dynamics of traveling waves. In fact, understanding of the bifurcation structure of the traveling wave solutions emerging in the unit-cell granular trimer is rather important and can shed light on the more complex nonlinear wave phenomena emerging in semi-infinite trimer chains. (c) 2016 Elsevier B.V. All rights reserved.

Influences of Hydration Force and Elastic Strain Energy on the Stability of Solid Film in a Very Thin Solid-on-Liquid Structure

Since hydration forces become very strong at short range and are particularly important for determining the magnitude of the adhesion between two surfaces or interaction energy, the influences of the hydration force and elastic strain energy due to hydration-induced layering of liquid molecules close to a solid film surface on the stability of a solid film in a solid-on-liquid (SOL) nanostructure are studied in this paper. The liquid of this thin SOL structure is a kind of water solution. Since the surface forces play an important role in the structure, the total free energy change of SOL structures consists of the changes in the bulk elastic energy within the solid film, the surface energy at the solid-liquid interface and the solid-air interface, and highly nonlinear volumetric component associated with interfacial forces. The critical wavelength of one-dimensional undulation, the critical thickness of the solid film, and the critical thickness of the liquid layer are studied, and the stability regions of the solid film have been determined. Emphasis is placed on calculation of critical values, which are the basis of analyzing the stability of the very thin solid film.

Analysis of residual stress gradient in MEMS multi-layer structure

Residual stress and its gradient through the thickness are among the most important properties of as-deposited films. Recently, a new mechanism based on a revised Thomas-Fermi-Dirac (TFD) model was proposed for the origin of intrinsic stress in solid film

Contingent sensitivity to configuration in a nonlinear evolution system

A trans-scopic sensitivity of macroscopic failure to slight differentiation in the meso-scopic structure of a system with nonlinear evolution is reported. A periodical chain following a non-local load-sharing evolution was applied as a propotype in failure study. The results demonstrate that there is a transition region composed of globally stable (GS) and evolution induced catastrophic (EIC) modes. That is different from a critical threshold as predicted by percolation and renormalization group theories. Moreover, the EIC mode shows a distinctive sample specific behaviour. For instance, some neighbouring initial states may evolve into completely different final states, though different initial states can evolve into the same final states. As an example, a marginal configuration of EIC mode, a quasi-Fibonacci skeleton, is constructed.

Structure-flexoelastic properties of bimesogenic liquid crystals

In this paper, we report on the flexoelastic and viscoelastic ratios for a number of bimesogens compounds with the same generic structure. Values are obtained indirectly by measuring the flexoelectro-optic response in the chiral nematic phase. By varying the molecular structure we alter the bend angle, transverse dipole moment, and length of the molecule. First, to examine the influence of the bend angle we use a homologous series whereby the only alteration in the molecular structure is the number of methylene units in the aliphatic spacer, n. Results show that the flexoelastic ratio, e K, and the effective flexoelectric coefficient, e, both exhibit an odd-even effect with values for n=odd being greater than that for n=even. This is understood in terms of an increase in the bend angle of the molecule and an increase in the transverse dipole moment. Second, in order to investigate the impact of the dipole moment, we have altered the mesogenic units so as to vary the longitudinal dipole moment and used different linkages in the aliphatic spacer in an attempt to alter the transverse dipole moment. Qualitatively, the results demonstrate that the odd-spaced bimesogen with larger transverse dipole moments exhibit larger flexoelastic ratios. © 2007 The American Physical Society.

Modelling nonlinear vehicle dynamics with neural networks

The nonlinear modelling ability of neural networks has been widely recognised as an effective tool to identify and control dynamic systems, with applications including nonlinear vehicle dynamics which this paper focuses on using multi-layer perceptron networks. Existing neural network literature does not detail some of the factors which effect neural network nonlinear modelling ability. This paper investigates into and concludes on required network size, structure and initial weights, considering results for networks of converged weights. The paper also presents an online training method and an error measure representing the network's parallel modelling ability over a range of operating conditions. Copyright © 2010 Inderscience Enterprises Ltd.

Nonlinear analysis of pile foundation jacket platform

In this paper, the nonlinear collapse of the BOHAI-8 pile foundation jacket platform has been analyzed. The ultimate load and collapse process of two computational models of the structure are given. One model is of fixed support whose length is eight times the pile leg diameter and the other considers the nonlinearity of the soil-pile interaction.

Equilibrium of isolated magnetostatic flux structure

Two-dimensional magnetostatic models of flux structure confined in stratified atmosphere are discussed in the present paper. The magnetic field in the flux structure is assumed to be force-free at the first step. Numerical solutions for this nonlinear free boundary problem are obtained by finite element method. Results show clearly the relation between the inside fields and outside pressure, especially the influence of atmospheric pressure distribution on the flux structure.

The geometric structure and dynamic properties of lauwerier attractor

 Introduction The strange chaotic attractor (ACS) is an important subject in the nonlinear field. On the basis of the theory of transversal heteroclinic cycles, it is suggested that the strange attractor is the closure of the unstable manifolds of countable infinite hyperbolic periodic points. From this point of view some nonlinear phenomena are explained reasonably. 更多还原

A Non-Parametric Dimension Test of the Term Structure

Published as an article in: Studies in Nonlinear Dynamics & Econometrics, 2004, vol. 8, issue 3, article 6.

Switching Regimes in the Term Structure of Interest Rates During U.S. Post-War: A case for the Lucas proof equilibrium?

Published as an article in: Studies in Nonlinear Dynamics & Econometrics, 2004, vol. 8, issue 1, pages 5.

Nonlinear Dynamic Response of Tension Leg Platform

Tension Leg Platform (TLP) is a typical compliant offshore structure for oil exploitation in deep water. Most of the existing mathematical models for analyzing the dynamic response of TLP are based on explicit or implicit assumptions that displacements (translations and rotations) are small magnitude. Herein a theoretical method for analyzing the nonlinear dynamic behavior of TLP with finite displacement is developed, in which multifold nonlinearities are taken into account, i.e. finite displacement, coupling of the six degrees of freedom, instantaneous position, instantaneous wet surface, free surface effects and viscous drag force. Using this theoretical model, we perform the numerical analysis of dynamic response of a representative TLP. The comparison between the degenerative linear solution of the proposed nonlinear model and the published one shows good agreements. Furthermore, numerical results are presented which illustrate that nonlinearities exert a distinct influence on the dynamic responses of the TLP.

Nonlinear Dynamic Responses of the Tensioned Tether under Parametric Excitations

The nonlinear dynamic responses of the tensioned tether subjected to combined surge and heave motions of floating platform are investigated using 2-D nonlinear beam model. It is shown that if the transverse-axial coupling of nonlinear beam model and the combined surge-heave motions of platform are considered, the governing equation is not Mathieu equation any more, it becomes nonlinear Hill equation. The Hill stability chart is obtained by using the Hill's infinite determinant and harmonic balance method. A parameter M, which is the function of tether length, the surge and heave amplitude of platform, is defined. The Hill stability chart is obviously different from Mathieu stability chart which is the specific case as M=0. Some case studies are performed by employing linear and nonlinear beam model respectively. It can be found that the results differences between nonlinear and linear model are apparent.

Changes in the size structure of the yellowfin tuna population of the tropical eastern Pacific Ocean from 1947 to 1955

ENGLISH: Morphometric studies by Godsil (1948), Godsil and Greenhood (1951), Royce (1953) and Schaefer (1952, 1955) have indicated that the yellowfin tuna of the Eastern Pacific are distinct from those of the Central Pacific. Tagging of yellowfin tuna by the California Department of Fish and Game, and by the Inter-American Tropical Tuna Commission in the Eastern Pacific, and by the Pacific Oceanic Fishery Investigations in the Central Pacific, have not yet revealed any migrations between these areas. Shimada and Schaefer (1956) have compared changes in population abundance and fishing intensity, considering the population in the Eastern Pacific as a separate entity. They conclude " ... the amount of fishing has had a real effect upon the stock of Eastern Pacific yellowfin tuna, taken in the aggregate, over the period studied. The evidence suggests also that for this species the intensity of fishing in some recent years has reached and might have even exceeded the level corresponding to the maximum equilibrium yield." Tagging experiments by the California Department of Fish and Game and by the Inter-American Tropical Tuna Commission have yielded returns in the order of one to five percent (Roedel 1954, and unpublished data of both agencies), a level much lower than that at which fishing intensity would be expected to noticeably affect the population size. These results are probably a reflection of the inadequacies of the present tagging methods, but they could lend doubt to the conclusions of Shimada and Schaefer. It is desirable, therefore, to examine other, independent, evidence as to the effects of fishing on the population. At the high levels of fishing intensity suggested by Shimada and Schaefer, in addition to changes in quantity, measurable changes would be expected to have occurred in the quality of the yellowfin tuna stocks, because the average age and size of the fish would have been reduced by the high mortality rates accompanying high fishing intensities. A continuing regular program of sampling catches and determining their length composition, to assess changes in the size composition of the stocks, was initiated by the Commission in 1954 but direct measurements are not available for the earlier, more dynamic period of growth of the fishery. Consequently, other, more general indications of possible changes in the size composition were sought. SPANISH: Los estudios morfométricos efectudos por Godsil (1948), Godsil y Greenhood (1951), Royce (1953) y Schaefer (1952, 1955), han demostrado que el atún aleta amarilla del Pacífico Oriental es distinto del que habita el PacÍfico Central. Los experimentos del Departamento de Pesca y Caza de California y de la Comisión Interamericana del Atún Tropical en el Pacífico Oriental, así como los de las Investigaciones Pesqueras del Océano Pacífico en el Pacífico Central,consistentes en la marcación de atunes aleta amarilla, aún no han puesto de manifiesto movimientos migratorios entre dichas áreas. Shimada y Schaefer (1956) han hecho estudios comparativos sobre la abundancia de la población y la intensidad de la pesca, considerando a la población del Pacífico Oriental como una entidad separada. Su conclusión es que " ... la intensidad de la pesca ha tenido un definido efecto sobre la población del atún aleta amarilla del Pacífico Oriental, tomada en conjunto, a lo largo del período estudiado. La evidencia de que se dispone sugiere así mismo que, por lo que hace a esta especie, la intensidad de la pesca en los últimos años ha alcanzado y quizás aún sobrepasado el nivel correspondiente a la máxima pesca de equilibrio". Los experimentos de mar•cación del Departamento de Pesca y Caza de California y de la Comisión Interamericana del Atún Tropical han producido recuperaciones ,entre el uno y el cinco por ciento (Roedel 1954 y datos inéditos de ambos organismos), lo que constituye un nivel mucho más bajo de aquél en que la intensidad de la pesca podría considerarse que afectaría notablemente el tamaño de la población. Estos resultados reflejan probablemente lo inadecuados que son aún los métodos de marcación, pero ellos podrían, quizá, poner en tela de juicio las conclusiones de Shimada y Schaefer. Por lo tanto,es deseable examinar otras fuentes de evidencia independientes, relacionadas con el efecto que la pesca tiene sobre la población. En efecto, si los altos índices de pesca sugeridos por Shimada y Schaefer son correctos, es de esperar que, además de los cambios en la magnitud de la población, se hayan producido otros, concomitantes y sensibles, en la calidad de los stocks de atún aleta amarilla, puesto que tanto el promedio de edad como el de tamaño de los individuos habrían disminuído debido a las elevadas tasas de mortalidad inherentes a las altas intensidades de pesca. En 1954 la Comisión inició un programa ininterrumpido para tomar muestras y determinar en ellas las frecuencias de tallas y evaluar de este modo los cambios correlativos que tuvieran lugar en los stocks pero, infortunadamente, este sistema de evaluación directa no fué practicado en el período anterior, que fué precisamente el de rápida expansión de la pesquería. En tal virtud, hubo de ser necesario buscar indicios más generales referentes a los cambios posibles en la composición de tamaños. (PDF contains 20 pages.)

Subdiffusion of nonlinear waves in quasiperiodic potentials

19 p.