Effective elasticity and persistence of strain in active filament-motor assemblies

Cross-linked, elastic, filamentous networks that are deformed by active molecular motors feature in several natural and synthetic settings. The effective active elasticity of these composite systems determines the length scale over which active deformations persist in fluctuating environments. This fundamental quantity has been studied in passive systems; however mechanisms determining and modulating this length-scale in active systems has not been clarified. Here, focusing on active arrayed filament-motor assemblies, we propose and analyze a minimal model in order to estimate the length scale over which imposed or emergent elastic deformations or stresses persist. We combine a mean-field continuum theory valid for weakly elastic assemblies with high dimensional Multi-Particle Collision (MPC) based Brownian simulations valid for moderate to strongly elastic and noisy systems. Integrating analytical and numerical results, we show that localized strains - steady or oscillatory - persist over well-defined length scales that dependent on motor activity, effective shear elasticity and filament extensibility. Extensibility is key even in very stiff filaments, and cannot be ignored when global deformations are considered. We clarify mechanisms by which motor derived active elasticity and passive shear elasticity of the filamentous backbone combine to effectively soften filaments. Surprisingly, the predictions of the mean-field theory agree qualitatively with results from stochastic discrete filament-motor model, even for moderately strong noise. We also find that athermal motor noise impacts the overall duty ratio of the motors and thereby the persistence length in these driven assemblies. Our study demonstrates how correlated activity in natural ordered active matter possesses a finite range of influence with clear testable experimental implications.

Velocity of transverse sound oscillations in the metals

The Bohm–Staver description of sound waves in metals in the jellium model is generalized by taking into account not only the self-consistent electric field but also the second correlation moment of internal electric field that provides shear elasticity. The system of linearized equations that contains the second correlation moment of the field as a new variable is built. The wave equation is worked out and the velocities of longitudinal and transverse sound are found. The estimation of the field correlation value through the sublimation heat and the electronic Fermi-gas energy is offered for the metals. The velocities of transverse sound are found, which matches well the velocity obtained from the shear modules.

Shear Wave Elastography Based on Noise Correlation and Time Reversal

Shear wave elastography (SWE) relies on the generation and tracking of coherent shear waves to image the tissue's shear elasticity. Recent technological developments have allowed SWE to be implemented in commercial ultrasound and magnetic resonance imaging systems, quickly becoming a new imaging modality in medicine and biology. However, coherent shear wave tracking sets a limitation to SWE because it either requires ultrafast frame rates (of up to 20 kHz), or alternatively, a phase-lock synchronization between shear wave-source and imaging device. Moreover, there are many applications where coherent shear wave tracking is not possible because scattered waves from tissue’s inhomogeneities, waves coming from muscular activity, heart beating or external vibrations interfere with the coherent shear wave. To overcome these limitations, several authors developed an alternative approach to extract the shear elasticity of tissues from a complex elastic wavefield. To control the wavefield, this approach relies on the analogy between time reversal and seismic noise cross-correlation. By cross-correlating the elastic field at different positions, which can be interpreted as a time reversal experiment performed in the computer, shear waves are virtually focused on any point of the imaging plane. Then, different independent methods can be used to image the shear elasticity, for example, tracking the coherent shear wave as it focuses, measuring the focus size or simply evaluating the amplitude at the focusing point. The main advantage of this approach is its compatibility with low imaging rates modalities, which has led to innovative developments and new challenges in the field of multi-modality elastography. The goal of this short review is to cover the major developments in wave-physics involving shear elasticity imaging using a complex elastic wavefield and its latest applications including slow imaging rate modalities and passive shear elasticity imaging based on physiological noise correlation.

Oblique Incidence Ultrasonic Reflectometry Device Based on c-axis Tilted ScAlN Films for Evaluating Viscoelastic Properties of Liquids Above 100 MHz

Ultrasound-based evaluation of fluid properties allows for real-time measurement of small amounts of liquid samples. The ultrasonic reflection method is used to obtain the complex reflection coefficient, which can be used to evaluate the viscoelastic properties of liquids. However, this method has not been used with shear waves at frequencies above 100 MHz because shear-mode piezoelectric films are difficult to obtain at such frequencies. We propose using the oblique incidence reflectometry with quasi-shear waves excited by c-axis tilted scandium aluminum nitride (ScAlN) thin films to realize high-sensitivity evaluation of the viscoelastic properties of liquids in the above 100 MHz. In experiments, the shear elasticity and shear viscosity of glycerin solutions were estimated from their complex reflection coefficients.

Explaining the low-frequency shear elasticity of confined liquids

Experimental observations of unexpected shear rigidity in confined liquids, on very low frequency scales on the order of 0.01 to 0.1 Hz, call into question our basic understanding of the elasticity of liquids and have posed a challenge to theoretical models of the liquid state ever since. Here we combine the nonaffine theory of lattice dynamics valid for disordered condensed matter systems with the Frenkel theory of the liquid state. The emerging framework shows that applying confinement to a liquid can effectively suppress the low-frequency modes that are responsible for nonaffine soft mechanical response, thus leading to an effective increase of the liquid shear rigidity. The theory successfully predicts the scaling lawG′∼L−3for the low-frequency shear modulus of liquids as a function of the confinement length L, in agreement with experimental results, and provides the basis for a more general description of the elasticity of liquids across different time and length scales.