Weakly nonlinear acoustic wave propagation in a nonlinear orthotropic circular cylindrical waveguide

Nonlinear acoustic wave propagation is considered in an infinite orthotropic thin circular cylindrical waveguide. The modes are non-planar having small but finite amplitude. The fluid is assumed to be ideal and inviscid with no mean flow. The cylindrical waveguide is modeled using the Donnell's nonlinear theory for thin cylindrical shells. The approximate solutions for the acoustic velocity potential are found using the method of multiple scales (MMS) in space and time. The calculations are presented up to the third order of the small parameter. It is found that at some frequencies the amplitude modulation is governed by the Nonlinear Schrodinger Equation (NLSE). The first objective is to study the nonlinear term in the NLSE, as the sign of the nonlinear term determines the stability of the amplitude modulation. On the other hand, at other specific frequencies, interactions occur between the primary wave and its higher harmonics. Here, the objective is to identify the frequencies of the higher harmonic interactions. Lastly, the linear terms in the NLSE obtained using the MMS calculations are validated. All three objectives are met using an asymptotic analysis of the dispersion equation. (C) 2015 Acoustical Society of America.

Nonlinear Dynamics of a Rotating Flexible Link

This paper deals with the study of the nonlinear dynamics of a rotating flexible link modeled as a one dimensional beam, undergoing large deformation and with geometric nonlinearities. The partial differential equation of motion is discretized using a finite element approach to yield four nonlinear, nonautonomous and coupled ordinary differential equations (ODEs). The equations are nondimensionalized using two characteristic velocities-the speed of sound in the material and a velocity associated with the transverse bending vibration of the beam. The method of multiple scales is used to perform a detailed study of the system. A set of four autonomous equations of the first-order are derived considering primary resonances of the external excitation and one-to-one internal resonances between the natural frequencies of the equations. Numerical simulations show that for certain ranges of values of these characteristic velocities, the slow flow equations can exhibit chaotic motions. The numerical simulations and the results are related to a rotating wind turbine blade and the approach can be used for the study of the nonlinear dynamics of a single link flexible manipulator.

Environmental Mechanics Research in China

By recalling mankind's path during past 50 years in the present article, we mainly highlight the significance of environmental issues today. In particular, two major factors leading to environment deterioration in China such as water resources and coal burning are stressed on. Present-day environmental issues are obviously interdisciplinary, of multiple scales and multi-composition in nature. Therefore, a process-based approach for environment research is absolutely necessarily. A series of sub-processes, either physical, chemical or biological, are subsequently analyzed in order to established reasonable parameterization scheme and credible comprehensive model. And we are now in a position to answer questions still open to us, improve existing somewhat empirical engineering approaches and enhance quantitative accuracy in prediction. To illustrate this process-based research approach, three typical examples associated with the Yangtze River Estuary, Loess Plateau and Tenggeli Desert environments have been dealt with respectively. A theoretical model of vertical flow field accounting for runoff and tide interaction has been established to delineate salinity and sediment motion which are responsible for the formation of mouth bar at the outlet and the ecological evolution there. A kinematic wave theory combined with the revised Green-Ampt infiltration formula is applied to the prediction of runoff generation and erosion in three types of erosion region on the Loess Plateau. Three approaches describing water motion in SPAC system in arid areas at different levels have been improved by introducing vegetation sub-models. However, we have found that the formation of a dry sandy layer and biological crust skin are additional primary causes leading to deterioration of water supply and succession of ecological system.

Synchronous Multi-Scale Observations on Rock Damage and Rupture

This paper reports a multi-scale study on damage evolution process and rupture of gabbro under uniaxial compression with several experimental techniques, including MTS810 testing machine, white digital speckle correlation method, and acoustic emission technique. In particular, the synchronization of the three experimental systems is realized for the study of relationship of deformation and damage at multiple scales. It is found that there are significant correlation between damage evolution at small and large length scales, and rupture at sample scale, especially it displays critical sensitivity at multiple scales and trans-scale fluctuations.

Sound transmission in strongly-curved slowly-varying cylindrical and annular lined ducts with flow

In this paper we consider the propagation of acoustic waves along a curved hollow or annular duct with lined walls. The curvature of the duct centreline and the wall radii vary slowly along the duct, allowing application of an asymptotic multiple scales analysis. This generalises Rienstra's analysis of a straight duct of varying cross-sectional radius. The result of the analysis is that the modal wavenumbers and mode shapes are determined locally as modes of a torus with the same local curvature, while the amplitude of the modes evolves as the mode propagates along the duct. The duct modes are found numerically at each axial location using a pseudo-spectral method. Unlike the case of a straight duct, there is a fundamental asymmetry between upstream and downstream propagating modes, with some mode shapes tending to be concentrated on either the inside or outside of the bend depending on the direction of propagation. The interaction between the presence of wall lining and curvature is investigated in particular; for instance, in a representative case it is found that the curvature causes the first few acoustic modes to be more heavily damped by the duct boundary than would be expected for a straight duct. Analytical progress can be made in the limit of very high mode order, in which case well-known 'whispering gallery' modes, localised close to the wall, can be identified.

A Nonlinear Threshold Model Applied to Spallation Analysis

Spallation in heterogeneous media is a complex, dynamic process. Generally speaking, the spallation process is relevant to multiple scales and the diversity and coupling of physics at different scales present two fundamental difficulties for spallation modeling and simulation. More importantly, these difficulties can be greatly enhanced by the disordered heterogeneity on multi-scales. In this paper, a driven nonlinear threshold model for damage evolution in heterogeneous materials is presented and a trans-scale formulation of damage evolution is obtained. The damage evolution in spallation is analyzed with the formulation. Scaling of the formulation reveals that some dimensionless numbers govern the whole process of deformation and damage evolution. The effects of heterogeneity in terms of Weibull modulus on damage evolution in spallation process are also investigated.

Critical Sensitivity and Trans-Scale Fluctuations in Catastrophic Rupture

Rupture in the heterogeneous crust appears to be a catastrophe transition. Catastrophic rupture sensitively depends on the details of heterogeneity and stress transfer on multiple scales. These are difficult to identify and deal with. As a result, the threshold of earthquake-like rupture presents uncertainty. This may be the root of the difficulty of earthquake prediction. Based on a coupled pattern mapping model, we represent critical sensitivity and trans-scale fluctuations associated with catastrophic rupture. Critical sensitivity means that a system may become significantly sensitive near catastrophe transition. Trans-scale fluctuations mean that the level of stress fluctuations increases strongly and the spatial scale of stress and damage fluctuations evolves from the mesoscopic heterogeneity scale to the macroscopic scale as the catastrophe regime is approached. The underlying mechanism behind critical sensitivity and trans-scale fluctuations is the coupling effect between heterogeneity and dynamical nonlinearity. Such features may provide clues for prediction of catastrophic rupture, like material failure and great earthquakes. Critical sensitivity may be the physical mechanism underlying a promising earthquake forecasting method, the load-unload response ratio (LURR).

Automated, objective texture segmentation of multibeam echosounder data - Seafloor survey and substrate maps from James Island to Ozette Lake, Washington Outer Coast

Without knowledge of basic seafloor characteristics, the ability to address any number of critical marine and/or coastal management issues is diminished. For example, management and conservation of essential fish habitat (EFH), a requirement mandated by federally guided fishery management plans (FMPs), requires among other things a description of habitats for federally managed species. Although the list of attributes important to habitat are numerous, the ability to efficiently and effectively describe many, and especially at the scales required, does not exist with the tools currently available. However, several characteristics of seafloor morphology are readily obtainable at multiple scales and can serve as useful descriptors of habitat. Recent advancements in acoustic technology, such as multibeam echosounding (MBES), can provide remote indication of surficial sediment properties such as texture, hardness, or roughness, and further permit highly detailed renderings of seafloor morphology. With acoustic-based surveys providing a relatively efficient method for data acquisition, there exists a need for efficient and reproducible automated segmentation routines to process the data. Using MBES data collected by the Olympic Coast National Marine Sanctuary (OCNMS), and through a contracted seafloor survey, we expanded on the techniques of Cutter et al. (2003) to describe an objective repeatable process that uses parameterized local Fourier histogram (LFH) texture features to automate segmentation of surficial sediments from acoustic imagery using a maximum likelihood decision rule. Sonar signatures and classification performance were evaluated using video imagery obtained from a towed camera sled. Segmented raster images were converted to polygon features and attributed using a hierarchical deep-water marine benthic classification scheme (Greene et al. 1999) for use in a geographical information system (GIS). (PDF contains 41 pages.)

Emergent synchronisation properties of a refrigerator demand side management system

In order to analyse the possibilities of improving grid stability on island systems by local demand response mechanisms,a multi-agent simulation model is presented. To support the primary reserve, an under-frequency load shedding (UFLS)using refrigerator loads is modelled. The model represents the system at multiple scales, by recreating each refrigerator individually, and coupling the whole population of refrigerators to a model which simulates the frequency response of the energy system, allowing for cross-scale interactions. Using a simple UFLS strategy, emergent phenomena appear in the simulation. Synchronisation e ects among the individual loads were discovered, which can have strong, undesirable impacts on the system such as oscillations of loads and frequency. The phase transition from a stable to an oscillating system is discussed.

The basque ecological debt: global socioecological impacts of a small open economy

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Multiscale habitat associations of deepwater demersal fishes off central California

Fish-habitat associations were examined at three spatial scales in Monterey Bay, California, to determine how benthic habitats and landscape configuration have structured deepwater demersal fish assemblages. Fish counts and habitat variables were quantified by using observer and video data collected from a submersible. Fish responded to benthic habitats at scales ranging from cm’s to km’s. At broad-scales (km’s), habitat strata classified from acoustic maps were a strong predictor of fish assemblage composition. At intermediate-scales (m’s−100 m’s), fish species were associated with specific substratum patch types. At fine-scales (<1 m), microhabitat associations revealed differing degrees of microhabitat specificity, and for some species revealed niche separation within patches. The use of habitat characteristics in ecosystembased management, particularly as a surrogate for species distributions, will depend on resolving fish-habitat associations and habitat complexity over multiple scales.

Multiscale object features from clustered complex wavelet coefficients

This paper introduces a method by which intuitive feature entities can be created from ILP (InterLevel Product) coefficients. The ILP transform is a pyramid of decimated complex-valued coefficients at multiple scales, derived from dual-tree complex wavelets, whose phases indicate the presence of different feature types (edges and ridges). We use an Expectation-Maximization algorithm to cluster large ILP coefficients that are spatially adjacent and similar in phase. We then demonstrate the relationship that these clusters possess with respect to observable image content, and conclude with a look at potential applications of these clusters, such as rotation- and scale-invariant object recognition. © 2005 IEEE.

Wave propagation in a slowly-varying duct with mean vortical swirling flow

The propagation of unsteady disturbances in a slowlyvarying cylindrical duct carrying mean swirling flow is investigated using a multiple-scales technique. This is applicable to turbomachinery flow behind a rotor stage when the swirl and axial velocities are of the same order. The presence of mean vorticity couples acoustic and vorticity equations which produces an eigenvalue problem that is not self-adjoint unlike that for irrotational mean flow. In order to determine the amplitude variation along the duct, an adjoint solution for the coupled system of equations is derived. The solution breaks down where a mode changes from cut on to cut off. In this region the amplitude is governed by a form of Airy's equation, and the effect of swirl is to introduce a small shift in the origin of the Airy function away from the turning-point location. The variation of axial wavenumber and amplitude along the duct is calculated. In hard-walled ducts mean swirl is shown to produce much larger amplitude variation along the duct compared with a nonswirling flow. Mean swirl also has a large effect in ducts with finite-impedance walls which differs depending on whether modes are co-rotating with the swirl or counter rotating. © 2001 by A.J. Cooper, Published by the American Institute of Aeronautics and Astronautics, Inc.

Second-harmonic generation of Bogoliubov excitations in a two-component Bose-Einstein condensate

A second-harmonic generation (SHG) is predicted for the Bogoliubov excitations in a two-component Bose-Einstein condensate. It is shown that, because the linear dispersion curve of the excitations displays two branches, the phase-matching condition for the SHG can be fulfilled if the wave vectors and frequencies of fundamental and second-harmonic waves are selected suitably from different branches. The nonlinearly coupled envelope equations for the SHG are derived by using a method of multiple scales. The explicit solutions of these envelope equations are provided and the conversion efficiency of the SHG is also discussed.

Solitary magnon excitations in a one-dimensional antiferromagnet with Dzyaloshinsky-Moriya interactions

We investigate solitary excitations in a model of a one-dimensional antiferromagnet including a single-ion anisotropy and a Dzyaloshinsky-Moriya antisymmetric exchange interaction term. We employ the Holstein-Primakoff transformation, the coherent state ansatz and the time variational principle. We obtain two partial differential equations of motion by using the method of multiple scales and applying perturbation theory. By so doing, we show that the motion of the coherent amplitude must satisfy the nonlinear Schrodinger equation. We give the single-soliton solution.