Estimating material viscoelastic properties based on surface wave measurements: a comparison of techniques and modeling assumptions

Previous studies of the first author and others have focused on low audible frequency (<1 kHz) shear and surface wave motion in and on a viscoelastic material comprised of or representative of soft biological tissue. A specific case considered has been surface (Rayleigh) wave motion caused by a circular disk located on the surface and oscillating normal to it. Different approaches to identifying the type and coefficients of a viscoelastic model of the material based on these measurements have been proposed. One approach has been to optimize coefficients in an assumed viscoelastic model type to match measurements of the frequency-dependent Rayleigh wave speed. Another approach has been to optimize coefficients in an assumed viscoelastic model type to match the complex-valued frequency response function (FRF) between the excitation location and points at known radial distances from it. In the present article, the relative merits of these approaches are explored theoretically, computationally, and experimentally. It is concluded that matching the complex-valued FRF may provide a better estimate of the viscoelastic model type and parameter values; though, as the studies herein show, there are inherent limitations to identifying viscoelastic properties based on surface wave measurements.     

Error propagation model for microscopic magnetic resonance elastography shear-wave images

Microscopic magnetic resonance elastography is a high-resolution method for visualizing shear waves and assessing the biomechanical viscoelastic properties of small biological samples. In this work, we used error propagation to develop a simple analytical model that relates the signal-to-noise ratio of MR magnitude images to the variance in shear-wave maps collected using gradient-echo and spin-echo phase-contrast pulse sequences. Our model predicts results for shear-wave images in phantoms, which match the experimentally observed phase variance within 8%. This model can be used to optimize MR pulse sequences for elastography studies, as well as other phase-difference techniques in MRI.     

Rayleigh-Lamb wave propagation on a fractional order viscoelastic plate

A previous study of the authors published in this journal focused on mechanical wave motion in a viscoelastic material representative of biological tissue [Meral et al., J. Acoust. Soc. Am. 126, 3278-3285 (2009)]. Compression, shear and surface wave motion in and on a viscoelastic halfspace excited by surface and sub-surface sources were considered. It was shown that a fractional order Voigt model, where the rate-dependent damping component that is dependent on the first derivative of time is replaced with a component that is dependent on a fractional derivative of time, resulted in closer agreement with experiment as compared with conventional (integer order) models, such as those of Voigt and Zener. In the present study, this analysis is extended to another configuration and wave type: out-of-plane response of a viscoelastic plate to harmonic anti-symmetric Lamb wave excitation. Theoretical solutions are compared with experimental measurements for a polymeric tissue mimicking phantom material. As in the previous configurations the fractional order modeling assumption improves the match between theory and experiment over a wider frequency range. Experimental complexities in the present study and the reliability of the different approaches for quantifying the shear viscoelastic properties of the material are discussed.     

Construction of low dissipative high-order well-balanced filter schemes for non-equilibrium flows

The goal of this paper is to generalize the well-balanced approach for non-equilibrium flow studied by Wang et al. (2009) [29] to a class of low dissipative high-order shock-capturing filter schemes and to explore more advantages of well-balanced schemes in reacting flows. More general 1D and 2D reacting flow models and new examples of shock turbulence interactions are provided to demonstrate the advantage of well-balanced schemes. The class of filter schemes developed by Yee et al. (1999) [33], Sjögreen and Yee (2004) [27] and Yee and Sjögreen (2007) [38] consist of two steps, a full time step of spatially high-order non-dissipative base scheme and an adaptive non-linear filter containing shock-capturing dissipation. A good property of the filter scheme is that the base scheme and the filter are stand-alone modules in designing. Therefore, the idea of designing a well-balanced filter scheme is straightforward, i.e. choosing a well-balanced base scheme with a well-balanced filter (both with high-order accuracy). A typical class of these schemes shown in this paper is the high-order central difference schemes/predictor–corrector (PC) schemes with a high-order well-balanced WENO filter. The new filter scheme with the well-balanced property will gather the features of both filter methods and well-balanced properties: it can preserve certain steady-state solutions exactly; it is able to capture small perturbations, e.g. turbulence fluctuations; and it adaptively controls numerical dissipation. Thus it shows high accuracy, efficiency and stability in shock/turbulence interactions. Numerical examples containing 1D and 2D smooth problems, 1D stationary contact discontinuity problem and 1D turbulence/shock interactions are included to verify the improved accuracy, in addition to the well-balanced behavior.     

QCT-based vibrational collisional models applied to nonequilibrium nozzle flows

We investigate from a theoretical perspective structure and dynamics of Na clusters on a surface built from Ar layers grown on a metal support. The system is modeled by a hierarchical quantum-mechanical/molecular-mechanical (QM/MM) approach treating the cluster electrons with time-dependent density-functional theory, the Ar atoms classically, and the metal support as a continuous dielectric medium. Caution has been taken to describe properly the dynamical polarizability of the Ar substrate. We study the effect of the Ar substrate and particularly of the metal support on the cluster structure and dynamics. The binding of Na₆ and Na₈ to the Ar surface is found to by very weak and the effect of the dielectric response of the metal (DRM) turns out to be negligible. The global properties of the optical response of the Na clusters are slightly changed by the Ar substrate and the DRM while the detailed spectral fragmentation depends sensitively on any change of the environment. The deposition dynamics of small Na clusters is crucially influenced by the mechanical hardness of the metal support while the DRM makes little effect. We also study the dependence on the number of Ar layers. For the first few layers (from two to four), the deposition dynamics changes dramatically with the number of layers. The results stabilize from six layers on upwards.     

Vorbereitungen für die Jahrtausend-Party

Around the world, BASF has been preparing for Y2K since 1996. The Information services and the Process Control Technology divisions, as well as embedded systems and logistics, not to mention the company's customers and suppliers have all been systenmatically tested for Y2K capability. In addition, special precautionary measures in particular, at large Verbund sites – will be in place during the switchover period.     

Spin Chemistry Investigation of Peculiarities of Photoinduced Electron Transfer in Donor–Acceptor Linked System

Photoinduced intramolecular electron transfer in linked systems, (R,S)- and (S,S)-naproxen-N-methylpyrrolidine dyads, has been studied by means of spin chemistry methods [magnetic field effect and chemically induced dynamic nuclear polarization (CIDNP)]. The relative yield of the triplet state of the dyads in different magnetic field has been measured, and dependences of the high-field CIDNP of the N-methylpyrrolidine fragment on solvent polarity have been investigated. However, both (S,S)- and (R,S)-enantiomers demonstrate almost identical CIDNP effects for the entire range of polarity. It has been demonstrated that the main peculiarities of photoprocesses in this linked system are connected with the participation of singlet exciplex alongside with photoinduced intramolecular electron transfer in chromophore excited state quenching.