Asymptotic wavenumber expansions of a strongly orthotropic fluid-filled circular cylindrical shell

In this paper, a suitable nondimensional `orthotropy parameter' is defined and asymptotic expansions are found for the wavenumbers in in vacuo and fluid-filled orthotropic circular cylindrical shells modeled by the Donnell-Mushtari theory. Here, the elastic moduli in the two directions are greatly different; the particular case of E-x >> E-theta is studied in detail, i.e., the elastic modulus in the longitudinal direction is much larger than the elastic modulus in the circumferential direction. These results are compared with the corresponding results for a `slightly orthotropic' shell (E-x approximate to E-theta) and an isotropic shell. The novelty of this presentation lies in obtaining closed-form expansions for the in vacuo and coupled wavenumbers in an orthotropic shell using perturbation methods aiding in a better physical understanding of the problem.

Asymptotic expansions for the structural wavenumbers of isotropic and orthotropic fluid-filled circular cylindrical shells in the intermediate frequency range

We consider wavenumbers in in vacuo and fluid-filled isotropic and orthotropic shells. Using the Donnell-Mushtari (DM) theory we find compact and elegant asymptotic expansions for the wavenumbers in the intermediate frequency range, i.e., around the ring frequency. This frequency range corresponds to the frequencies where there is a rapid change in the values of bending wavenumbers and is found to exist in isotropic and orthotropic shells (in vacua and fluid-filled) for low circumferential orders n only. The same is first identified using the n=0 mode of an orthotropic shell. Following this, using the expression for the intermediate frequency, asymptotic expansions are found for other cases. Here, in order to get compact expansions we consider slight orthotropy (epsilon << 1) and light fluid loading (mu << 1). Thus, the orthotropy parameter epsilon and the fluid loading parameter mu are used as asymptotic parameters along with the non-dimensional thickness parameter beta. The methodology can be extended to any order of epsilon, only the expansions become unwieldy. The expansions are matched with the numerical solutions of the corresponding dispersion relation. The match is found to be good.

Expansions of tau hadronic spectral function moments in a nonpower QCD perturbation theory with tamed large order behavior

The moments of the hadronic spectral functions are of interest for the extraction of the strong coupling alpha(s) and other QCD parameters from the hadronic decays of the tau lepton. Motivated by the recent analyses of a large class of moments in the standard fixed-order and contour-improved perturbation theories, we consider the perturbative behavior of these moments in the framework of a QCD nonpower perturbation theory, defined by the technique of series acceleration by conformal mappings, which simultaneously implements renormalization-group summation and has a tame large-order behavior. Two recently proposed models of the Adler function are employed to generate the higher-order coefficients of the perturbation series and to predict the exact values of the moments, required for testing the properties of the perturbative expansions. We show that the contour-improved nonpower perturbation theories and the renormalization-group-summed nonpower perturbation theories have very good convergence properties for a large class of moments of the so-called ``reference model,'' including moments that are poorly described by the standard expansions. The results provide additional support for the plausibility of the description of the Adler function in terms of a small number of dominant renormalons.

Taylor series expansion based multidimensional image reconstruction for confocal and 4pi microscopy

We propose and experimentally demonstrate a three-dimensional (3D) image reconstruction methodology based on Taylor series approximation (TSA) in a Bayesian image reconstruction formulation. TSA incorporates the requirement of analyticity in the image domain, and acts as a finite impulse response filter. This technique is validated on images obtained from widefield, confocal laser scanning fluorescence microscopy and two-photon excited 4pi (2PE-4pi) fluorescence microscopy. Studies on simulated 3D objects, mitochondria-tagged yeast cells (labeled with Mitotracker Orange) and mitochondrial networks (tagged with Green fluorescent protein) show a signal-to-background improvement of 40% and resolution enhancement from 360 to 240 nm. This technique can easily be extended to other imaging modalities (single plane illumination microscopy (SPIM), individual molecule localization SPIM, stimulated emission depletion microscopy and its variants).

Asymptotics of Harish-Chandra expansions, bounded hypergeometric functions associated with root systems, and applications

A series expansion for Heckman-Opdam hypergeometric functions phi(lambda) is obtained for all lambda is an element of alpha(C)*. As a consequence, estimates for phi(lambda) away from the walls of a Weyl chamber are established. We also characterize the bounded hypergeometric functions and thus prove an analogue of the celebrated theorem of Helgason and Johnson on the bounded spherical functions on a Riemannian symmetric space of the noncompact type. The L-P-theory for the hypergeometric Fourier transform is developed for 0 < p < 2. In particular, an inversion formula is proved when 1 <= p < 2. (C) 2013 Elsevier Inc. All rights reserved.

Asymptotic expansions for wavenumbers in orthotropic fluid-filled circular cylindrical shells for intermediate fluid loading

Coupled wavenumbers in infinite fluid-filled isotropic and orthotropic cylindrical shells are considered. Using the Donnell-Mushtari (DM) theory for thin shells, compact and elegant asymptotic expansions for the wavenumbers are found at an intermediate fluid loading for both the coupled rigid-duct modes (''fluid-originated'') and the coupled structural wavenumbers (''structure-originated modes'') over the entire frequency range where DM theory is valid. The coupled rigid-duct expansions are found to be valid for O(1) orthotropy and for all circumferential orders, whereas the coupled structural wavenumber expansions are valid for small orthotropy and for low circumferential orders. These two above results are then used to derive the expansions for a set of multiple complex roots that display a locking behavior at this intermediate fluid-loading. The expansions are matched with the numerical solutions of the coupled dispersion relation and the match is found to be good over most of the frequency range. (C) 2014 Acoustical Society of America.

Nonlinear viscoelasticity of entangled wormlike micellar fluid under large-amplitude oscillatory shear: Role of elastic Taylor-Couette instability

The role of elastic Taylor-Couette flow instabilities in the dynamic nonlinear viscoelastic response of an entangled wormlike micellar fluid is studied by large-amplitude oscillatory shear (LAOS) rheology and in situ polarized light scattering over a wide range of strain and angular frequency values, both above and below the linear crossover point. Well inside the nonlinear regime, higher harmonic decomposition of the resulting stress signal reveals that the normalized third harmonic I-3/I-1 shows a power-law behavior with strain amplitude. In addition, I-3/I-1 and the elastic component of stress amplitude sigma(E)(0) show a very prominent maximum at the strain value where the number density (n(v)) of the Taylor vortices is maximum. A subsequent increase in applied strain (gamma) results in the distortions of the vortices and a concomitant decrease in n(v), accompanied by a sharp drop in I-3 and sigma(E)(0). The peak position of the spatial correlation function of the scattered intensity along the vorticity direction also captures the crossover. Lissajous plots indicate an intracycle strain hardening for the values of gamma corresponding to the peak of I-3, similar to that observed for hard-sphere glasses.

Wave propagation in a 2D nonlinear structural acoustic waveguide using asymptotic expansions of wavenumbers

Nonlinear acoustic wave propagation in an infinite rectangular waveguide is investigated. The upper boundary of this waveguide is a nonlinear elastic plate, whereas the lower boundary is rigid. The fluid is assumed to be inviscid with zero mean flow. The focus is restricted to non-planar modes having finite amplitudes. The approximate solution to the acoustic velocity potential of an amplitude modulated pulse is found using the method of multiple scales (MMS) involving both 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 here is to study the nonlinear term in the NLSE. The sign of the nonlinear term in the NLSE plays a role in determining the stability of the amplitude modulation. Secondly, at other frequencies, the primary pulse interacts with its higher harmonics, as do two or more primary pulses with their resultant higher harmonics. This happens when the phase speeds of the waves match and the objective is to identify the frequencies of such interactions. For both the objectives, asymptotic coupled wavenumber expansions for the linear dispersion relation are required for an intermediate fluid loading. The novelty of this work lies in obtaining the asymptotic expansions and using them for predicting the sign change of the nonlinear term at various frequencies. It is found that when the coupled wavenumbers approach the uncoupled pressure-release wavenumbers, the amplitude modulation is stable. On the other hand, near the rigid-duct wavenumbers, the amplitude modulation is unstable. Also, as a further contribution, these wavenumber expansions are used to identify the frequencies of the higher harmonic interactions. And lastly, the solution for the amplitude modulation derived through the MMS is validated using these asymptotic expansions. (C) 2015 Elsevier Ltd. All rights reserved.

epsilon-expansions near three dimensions from conformal field theory

We formally extend the CFT techniques introduced in arXiv: 1505.00963, to phi(2d0/d0-2) theory in d = d(0) dimensions and use it to compute anomalous dimensions near d(0) = 3, 4 in a unified manner. We also do a similar analysis of the O(N) model in three dimensions by developing a recursive combinatorial approach for OPE contractions. Our results match precisely with low loop perturbative computations. Finally, using 3-point correlators in the CFT, we comment on why the phi(3) theory in d(0) = 6 is qualitatively different.

Rayleigh-Taylor instability in a thermocline based thermal storage tank

Numerical simulations are performed to study the stability characteristics of a molten salt thermocline storage unit. Perturbations are introduced into a stable flow field in such a way as to make the top-fluid heavier than the fluid at the bottom, thereby causing a possible instability in the system. The evolution pattern of the various disturbances are examined in detail. Disturbances applied for short duration get decayed before they could reach the thermocline, whereas medium and long duration disturbances evolve into a ``falling spike'' or ``stalactite-like'' structure and destabilize the thermocline. Rayleigh Taylor instability is observed inside the storage tank. The effect of the duration, velocity and temperature of the disturbance on thermocline thickness and penetration length are studied. A quadratic time dependence of penetration length was observed. New perspectives on thermocline breakdown phenomena are obtained from the numerical flow field. (C) 2015 Elsevier Masson SAS. All rights reserved.

Large-Eddy-Simulation of 3-Dimensional Rayleigh-Taylor Instability in Incompressible Fluids

The 3-dimensiqnal incompressible Rayleigh-Taylor instability is numerically studied through the large-eddy-simulation (LES) approach based on the passive scalar transport model. Both the instantaneous velocity and the passive scalar fields excited by sinu

Rayleigh-Taylor Instability of a Liquid Drop at High Bond Numbers

给出了高Bond数下黏性液滴表面Rayleigh-Taylor线性不稳定性的分析解,这种不稳定性对于超音速气流作用下液滴破碎的早期阶段起着至关重要的作用.基于稳定性分析的结果,导出了用于估算稳定液滴的最大直径及液滴无量纲初始破碎时间的计算式,这些计算式与相关文献给出的实验和分析结果比较显示了良好的一致.

拟压缩性方法在非定常球形Couette-Taylor流模拟中的应用

本文以拟压缩性法和物理时间/伪时间双重时间推进,数值求解非定常不可压缩流N=S方程。拟压缩性项是对伪时间的导数项,在每一物理时间层,进行对伪时间的推进使拟压缩性项趋于零,从而使连续方程得到满足。用Lower-Upper Symmetric Gaus-—Seidel(LU-SGS)恪式求解离散所得的方程。针对前人LU-SGS格式未计及隐式物理粘性,在计算中低Re数流动时容易发散或造成收敛率低的问题,利用简化的隐式粘性项改善了格式的稳定性,并用三阶迎风紧致差分逼近无粘通量,提高了伪时间推进的收敛率。模拟了间隙比σ=0.18的两同心旋转球之间轴对称Couette-Taylor流的0-、1-和2-涡三种流态和它们之间的转变过程。