On the distance to blow-up of acceleration waves in random media

We study the effects of material spatial randomness on the distance to form shocks from acceleration waves, , in random media. We introduce this randomness by taking the material coefficients and – that represent the dissipation and elastic nonlinearity, respectively, in the governing Bernoulli equation – as a stochastic vector process. The focus of our investigation is the resulting stochastic, rather than deterministic as in classical continuum mechanics studies, competition of dissipation and elastic nonlinearity. Quantitative results for are obtained by the method of moments in special simple cases, and otherwise by the method of maximum entropy. We find that the effect of even very weak random perturbation in and may be very significant on . In particular, the full negative cross-correlation between and $ results in the strongest scatter of , and hence, in the largest probability of shock formation in a given distance x. Received November 6, 2001 / Published online September 4, 2002 Dedicated to Professor Ingo Müller on the occasion of his 65th birthday Communicated by Kolumban Hutter, Darmstadt     

Time reversal for obstacle location in elastodynamics from acoustic recording

The Note is concerned with a feasibility study of time reversal in a non-homogeneous elastic medium, from data recorded in an acoustic medium. Our aim here is to determine the presence and some physical properties of elastic “inclusions” (unknown, not observable solid objects, characterized by their elastic properties) from partial observations of acoustic waves scattered by these inclusions. A finite element numerical method, based on a variational acousto-elastodynamics formulation, is derived and used to solve the forward, and then, the time-reversed problem. A criterion, derived from the reverse time migration framework, is introduced, to help construct images of the inclusions to be determined. Numerical illustrations on configurations that mimic the breast cancer configuration are proposed, and show that one can differentiate between two inclusions, even with different properties.     

Parametric interaction of acoustic waves in micro-inhomogeneous media with hysteretic nonlinearity and relaxation

A theoretical investigation of parametric processes that arise as a result of the interaction of powerful and weak longitudinal acoustic waves in micro-inhomogeneous media with hysteretic nonlinearity and relaxation was carried out. The case of degenerate interaction between a powerful high-frequency wave and a weak low-frequency one was considered. The nonlinear damping coefficient and the carrier frequency phase delay of the weak wave propagating under the action of the powerful wave were determined.     

Homogenization of acoustic waves in strongly heterogeneous porous structures

We consider acoustic waves in fluid-saturated periodic media with dual porosity. At the mesoscopic level, the fluid motion is governed by the Darcy flow model extended by inertia terms and by the mass conservation equation. In this study, assuming the porous skeleton is rigid, the aim is to distinguish the effects of the strong heterogeneity in the permeability coefficients. Using the asymptotic homogenization method we derive macroscopic equations and obtain the dispersion relationship for harmonic waves. The double porosity gives rise to an extra homogenized coefficient of dynamic compressibility which is not obtained in the upscaled single porosity model. Both the single and double porosity models are compared using an example illustrating wave propagation in layered media.     

Dynamic behavior of piles embedded in transversely isotropic layered media

Dynamic behavior of single pile embedded in transversely isotropic layered media is investigated using the finite element method combined with dynamic stiffness matrices of the soil derived from Green's function for ring loads. The influence of soil anisotropy on the dynamic behavior of piles is examined through a series of parametric studies     

Acoustic, thermal and flow processes in a water filled nanoporous glass by time-resolved optical spectroscopy

We present heterodyne detected transient grating measurements on water filled Vycor 7930 in the range of temperature 20-90 °C. This experimental investigation enables to measure the acoustic propagation, the average density variation due to the liquid flow and the thermal diffusion in this water filled nano-porous material. The data have been analyzed with the model of Pecker and Deresiewicz which is an extension of Biot model to account for the thermal effects. In the whole temperature range the data are qualitatively described by this hydrodynamic model that enables a meaningful insight of the different dynamic phenomena. The data analysis proves that the signal in the intermediate and long time-scale can be mainly addressed to the water dynamics inside the pores. We proved the existence of a peculiar interplay between the mass and the heat transport that produces a flow and back-flow process inside the nano-pores. During this process the solid and liquid dynamics have opposite phase as predicted by the Biot theory for the slow diffusive wave. Nevertheless, our experimental results confirm that transport of elastic energy (i.e. acoustic propagation), heat (i.e. thermal diffusion) and mass (i.e. liquid flow) in a liquid filled porous glass can be described according to hydrodynamic laws in spite of nanometric dimension of the pores. The data fitting, based on the hydrodynamic model, enables the extraction of several parameters of the water-Vycor system, even if some discrepancies appear when they are compared with values reported in the literature.     

Numerical simulation of three-dimensional saturated flow in randomly heterogeneous porous media

This paper presents a numerical method for simulating flow fields in a stochastic porous medium that satisfies locally the Darcy equation, and has each of its hydraulic parameters represented as one realization of a three-dimensional random field. These are generated by using the Turning Bands method. Our ultimate objective is to obtain statistically meaningful solutions in order to check and extend a series of approximate analytical results previously obtained by a spectral perturbation method (L. W. Gelhar and co-workers). We investigate the computational aspects of the problem in relation with stochastic concepts. The difficulty of the numerical problem arises from the random nature of the hydraulic conductivities, which implies that a very large discretized algebraic system must be solved. Indeed, a preliminary evaluation with the aid of scale analysis suggests that, in order to solve meaningful flow problems, the total number of nodes must be of the order of 10⁶. This is due to the requirement that x _i gl _i L _i , where x _i is the mesh size, _i is a typical correlation scale of the inputs, and L _i is the size of the flow domain (i = 1, 2, 3). The optimum strategy for the solution of such a problem is discussed in relation with supercomputer capabilities. Briefly, the proposed discretization method is the seven-point finite differences scheme, and the proposed solution method is iterative, based on prior approximate factorization of the large coefficient matrix. Preliminary results obtained with grids on the order of one hundred thousand nodes are discussed for the case of steady saturated flow with highly variable, random conductivities.     

Body waves in fractured porous media saturated by two immiscible newtonian fluids

A study of body waves in fractured porous media saturated by two fluids is presented. We show the existence of four compressional and one rotational waves. The first and third compressional waves are analogous to the fast and slow compressional waves in Biot's theory. The second compressional wave arises because of fractures, whereas the fourth compressional wave is associated with the pressure difference between the fluid phases in the porous blocks. The effects of fractures on the phase velocity and attenuation coefficient of body waves are numerically investigated for a fractured sandstone saturated by air and water phases. All compressional waves except the first compressional wave are diffusive-type waves, i.e., highly attenuated and do not exist at low frequencies.Now at Izmir Institute of Technology, Faculty of Engineering, Gaziosmanpasa Bulvari, No.16, Cankaya, Izmir, Turkey.     

Monochromatic surface waves on impermeable boundaries in two-component poroelastic media

The dispersion relation for surface waves on an impermeable boundary of a fully saturated poroelastic medium is investigated numerically over the whole range of applicable frequencies. To this aim a linear simplified model of a two-component poroelastic medium is used. Similarly to the classical Biot’s model, it is a continuum mechanical model but it is much simpler due to the lack of coupling of stresses. However, results for bulk waves following for these two models agree very well indeed which motivates the application of the simplified model in the analysis of surface waves. In the whole range of frequencies there exist two modes of surface waves corresponding to the classical Rayleigh and Stoneley waves. The numerical results for velocities and attenuations of these waves are shown for different values of the bulk permeability coefficient in different ranges of frequencies. In particular, we expose the low and high frequency limits, and demonstrate the existence of the Stoneley wave in the whole range of frequencies as well as the leaky character of the Rayleigh wave.