Connecting the grain-shearing mechanism of wave propagation in marine sediments to fractional order wave equations

Hidden jerk in universal creep and aftershocks

Most materials exhibit creep memory under the action of a constant load. The memory behavior is governed by Andrade's creep law, which also has an inherent connection with the Omori-Utsu law of earthquake aftershocks. Both empirical laws lack a deterministic interpretation. Coincidentally, the Andrade law is similar to the time-varying part of the creep compliance of the fractional dashpot in anomalous viscoelastic modeling. Consequently, fractional derivatives are invoked, but since they lack a physical interpretation, the physical parameters of the two laws extracted from curve fit lack confidence. In this Letter, we establish an analogous linear physical mechanism that underlies both laws and relates its parameters with the material's macroscopic properties. Surprisingly, the explanation does not require the property of viscosity. Instead, it necessitates the existence of a rheological property that relates strain with the first order time derivative of stress, which involves jerk. Further, we justify the constant quality factor model of acoustic attenuation in complex media. The obtained results are validated in light of the established observations.

Hamilton's geoacoustic model

The Reflections series takes a look back on historical articles from The Journal of the Acoustical Society of America that have had a significant impact on the science and practice of acoustics.

Connecting the grain-shearing, creep, and squirt flow models for wave propagation in the seabed

The generalized creep and squirt flow models are shown to be stationary creep processes. A fractional exponent is used to develop a new generalized squirt flow model. The responses of the grain-shearing and generalized creep models are identical, although based on entirely different concepts: a single spring and time-varying damper versus a continuous distribution of parallel Maxwell elements. The random structure of marine sand is more consistent with the latter, implying absence of strain-hardening. The generalized squirt flow model has a high frequency cutoff suited to practical systems, limited by the speed with which underlying physical changes can occur.

Acoustic Mapping of Submerged Stone Age Sites—A HALD Approach

Acoustic response from lithics knapped by humans has been demonstrated to facilitate effective detection of submerged Stone Age sites exposed on the seafloor or embedded within its sediments. This phenomenon has recently enabled the non-invasive detection of several hitherto unknown submerged Stone Age sites, as well as the registration of acoustic responses from already known localities. Investigation of the acoustic-response characteristics of knapped lithics, which appear not to be replicated in naturally cracked lithic pieces (geofacts), is presently on-going through laboratory experiments and finite element (FE) modelling of high-resolution 3D-scanned pieces. Experimental work is also being undertaken, employing chirp sub-bottom systems (reflection seismic) on known sites in marine areas and inland water bodies. Fieldwork has already yielded positive results in this initial stage of development of an optimised Human-Altered Lithic Detection (HALD) method for mapping submerged Stone Age sites. This paper reviews the maritime archaeological perspectives of this promising approach, which potentially facilitates new and improved practice, summarizes existing data, and reports on the present state of development. Its focus is not reflection seismics as such, but a useful resonance phenomenon induced by the use of high-resolution reflection seismic systems.

Rheological determinants for simultaneous staging of hepatic fibrosis and inflammation in patients with chronic liver disease

The purpose of this study is to investigate the use of fundamental rheological parameters as quantified by MR elastography (MRE) to measure liver fibrosis and inflammation simultaneously in humans. MRE was performed on 45 patients at 3 T using a vibration frequency of 56 Hz. Fibrosis and inflammation scores were obtained from liver biopsies. Biomechanical properties were quantified in terms of complex shear modulus G* as well as shear wave phase velocity c and shear wave attenuation α. A rheological fractional derivative order model was used to investigate the linear dependence of the free model parameters (dispersion slope y, intrinsic speed c0 , and intrinsic relaxation time τ) on histopathology. Leave-one-out cross-validation was then utilized to demonstrate the effectiveness of the model. The intrinsic speed c0 increases with hepatic fibrosis, while an increased relaxation time τ is reflective of more inflammation of the liver parenchyma. The dispersion slope y does not depend either on fibrosis or on inflammation. The proposed rheological model, given this specific parameterization, establishes the functional dependences of biomechanical parameters on histological fibrosis and inflammation. The leave-one-out cross-validation demonstrates that the model allows identification, from the MRE measurements, of the histology scores when grouped into low-/high-grade fibrosis and low-/high-grade inflammation with significance levels of P = 0.0004 (fibrosis) and P = 0.035 (inflammation). The functional dependences of intrinsic speed and relaxation time on fibrosis and inflammation, respectively, shed new light onto the impact hepatic pathological changes on liver tissue biomechanics in humans. The dispersion slope y appears to represent a structural parameter of liver parenchyma not impacted by the severity of fibrosis/inflammation present in this patient cohort. This specific parametrization of the well-established rheological fractional order model is valuable for the clinical assessment of both fibrosis and inflammation scores, going beyond the capability of the plain shear modulus measurement commonly used for MRE.

Restrictions on wave equations for passive media

Most derivations of acoustic wave equations involve ensuring that causality is satisfied. Here, the consequences of also requiring that the medium should be passive are explored. This is a stricter criterion than causality for a linear system and implies that there are restrictions on the relaxation modulus and its first few derivatives. The viscous and relaxation models of acoustics satisfy passivity and have restrictions on not only a few, but all derivatives of the relaxation modulus. These models are described as a system of springs and dampers with positive parameters and belong to the important class of completely monotone systems. It is shown here that the attenuation as a function of frequency for such media has to increase slower than a linear function. Likewise, the phase velocity has to increase monotonically. This gives criteria on which one may judge whether a proposed wave equation is passive or not, as illustrated by comparing two different versions of the viscous wave equation.