Power-law Rheology Research Articles

Nonlinear power-law creep of cell cortex: A minimal model

Experiments have revealed that biological cells exhibit a universal power-law rheology, but the underlying mechanisms remain elusive. Here, we present a minimal model to explain the power-law creep of cell cortex, which is abstracted as chains of crosslinkers with random binding energies. Using this model, we show that when both the load and chain length are small, the logarithm of both the strain and time scales with the fraction of unbound crosslinkers, leading to power-law creep with a constant exponent, as observed in many experiments. Increasing the load alters the latter relationship between time and unbinding fraction, and thus, increases the power-law exponent, explaining the stress-induced nonlinearity in some experiments. Increasing the chain length alters this relationship as well, and as a result, the exponent grows proportionally with the chain length, explaining the crosslinker-density-induced nonlinearity in other experiments. This work provides a mesoscopic explanation for the linear and nonlinear power-law creep of cell cortex and may serve as a basis for understanding the cytoskeletal mechanics.

Postseismic deformation due to the 2021 MW 7.4 Maduo (China) earthquake and implications for regional rheology and seismic hazards around the Bayan Har block

GPS and InSAR observations of the first ∼1.5 years of postseismic deformation caused by the 2021 MW 7.4 Maduo earthquake provide a valuable opportunity to investigate fault interactions and regional rheological structure, as well as the future seismic potential around the Bayan Har block, northeastern Tibetan Plateau. We develop an integrated model to simulate the afterslip and viscoelastic relaxation contributions to the observed postseismic displacements, and found that afterslip driven by the coseismic stress is concentrated downdip of rupture, and dominates the postseismic deformation in the early stage (∼0.4 year after the event). Because afterslip decays quickly over time, viscoelastic relaxation should become the main postseismic mechanism as time goes on. The two mechanisms produce similar displacements during 0.4–1.5 years after the earthquake, but at 1.5 years after the earthquake the velocity caused by viscoelastic relaxation is larger than that caused by afterslip. Viscoelastic models assuming either a Burgers body or power-law rheology produce very similar predictions, with the Burgers body model having a slightly lower overall misfit. The rheological structure constrained by the postseismic observations supports the 35-km thick elastic upper crust overlying a Burgers body viscoelastic lower curst with a Maxwell viscosity of 3 × 1019 Pa s (5 - 50 × 1018 Pa s at 95% confidence), assuming the Kelvin viscosity is equal to 10% of that value. This is different from the regional rheology inferred by the postseismic investigations on the 2001 MW 7.8 Kokoxili and the 2008 MW 7.8 Wenchuan events, and the preferred thickness of the elastic crust is also different from that inferred from magnetotelluric profiles deployed in previous studies. We thus infer that the rheological structure within the Bayan Har block is possibly heterogeneous from west to east. Finally, the normal stress changes triggered by the coseismic rupture and postseismic process are estimated to be negative, but the shear stress changes to be positive on the western Kunlun fault, the eastern Dari fault and Bayan-Har Mountain fault. However, the current observations and studies are quite insufficient on those fault segments, therefore, we need to focus on their faulting behavior and seismic risk in the future.

Deciphering the complex mechanics of atherosclerotic plaques: A hybrid hierarchical theory-microrheology approach

Understanding the viscoelastic properties of atherosclerotic plaques at rupture-prone scales is crucial for assessing their vulnerability. Here, we develop a Hybrid Hierarchical theory-Microrheology (HHM) approach, enabling the analysis of multiscale mechanical variations and distribution changes in regional tissue viscoelasticity within plaques across different spatial scales. We disclose a universal two-stage power-law rheology in plaques, characterized by distinct power-law exponents (αshort and αlong), which serve as mechanical indexes for plaque components and assessing mechanical gradients. We further propose a self-similar hierarchical theory that effectively delineates plaque heterogeneity from the cytoplasm, cell, to tissue levels. Moreover, our proposed multi-layer perceptron model addresses the viscoelastic heterogeneity and gradients within plaques, offering a promising diagnostic strategy for identifying unstable plaques. These findings not only advance our understanding of plaque mechanics but also pave the way for innovative diagnostic approaches in cardiovascular disease management. Statement of significanceOur study pioneers a Hybrid Hierarchical theory-Microrheology (HHM) approach to dissect the intricate viscoelasticity of atherosclerotic plaques, focusing on distinct components including cap fibrosis, lipid pools, and intimal fibrosis. We unveil a universal two-stage power-law rheology capturing mechanical variations across plaque structures. The proposed hierarchical model adeptly captures viscoelasticity changes from cytoplasm, cell to tissue levels. Based on the newly proposed markers, we further develop a machine learning (ML) diagnostic model that sets precise criteria for evaluating plaque components and heterogeneity. This work not only reveals the comprehensive mechanical heterogeneity within plaques but also introduces a mechanical marker-based ML strategy for assessing plaque conditions, offering a significant leap towards understanding and diagnosing atherosclerotic risks.

Quantifying rheology and texture of chocolate products with oleogels using fractional calculus

Oleogels, a novel technology for structuring fats, show great potential for partially or completely replacing solid fats in chocolate products containing unhealthy saturated fatty acids. However, how to maintain similar rheological properties and sensory texture attributes is a major challenge. Given the lack of a concise and effective mathematical framework, simulating the rheological response and quantifying the textural parameters of the hybrid oleogel-dispersed chocolate products, is complicated. In this work, the rheological power law behavior of hybrid oleogel-dispersed chocolate products is accurately captured by using a fractional constitutive mathematical framework with few constitutive parameters. The sensory texture parameter firmness is quantified on the basis of creep response. The rheological response and firmness index are linked together on the basis of the fractional derivative model. This work helps provide heuristic insights into the structure-texture engineering of this food type. Such insights may, in turn, guide the formulation and design of food products.

Quantitative evaluation of mantle flow traction on overlying tectonic plate: linear versus power-law mantle rheology

SUMMARY Sub-plate mantle flow traction (MFT) has been considered as a major driving force for plate motion; however, the force acting on the overlying plate is difficult to constrain. One of the reasons lies in the variable rheological flow laws of mantle rocks, for example, linear versus power-law rheology, applied in previous studies. Here, systematic numerical models are conducted to evaluate MFT under variable rheological, geometrical and kinematic conditions. The results indicate that MFT with power-law rheology is much lower than that with linear rheology under the same mantle/plate velocity contrast. In addition, existence of a lithospheric root in the overlying plate could enhance MFT, where integrated normal force acting on the walls of lithospheric root is much lower than the shear force in a large-scale domain. In the acting domain of several thousand kilometres, MFT with power-law rheology is comparable to the ridge push of about 3×1012 N m−1, whereas that with linear rheology is comparable to the slab pull of about 3×1013 N m−1. The roles of MFT in driving plate motion are further analysed for the Tethyan evolution. It indicates that MFT with power-law rheology could partially support the Wilson cycles experienced in the Tethyan system, whereas that with linear rheology could easily dominate any kinds of plate tectonic evolutions. The quantitative evaluation of MFT in this study clarifies the roles of rheological flow laws on MFT and could help us to better understand the contrasting results in previous numerical studies.

Viscoelastic Mechanical Signature-Based Machine Learning for Assessment of Liver Fibrosis and Its Regression

Viscoelastic mechanical characteristics of the liver play a crucial role in fibrosis and cancer progression. Despite the evolution of liver fibrosis, as a pivotal step toward cirrhosis and hepatoma, originates from molecular dysfunctions and further extends to cellular and tissue levels, current clinical assessment is still largely based on tissue level stiffness. This study introduces a novel multiscale viscoelastic signature-based machine learning model for liver fibrosis evaluation. Utilizing a hybrid hierarchical theory-microrheology approach, we unveil a universal two-stage power-law rheology capturing dynamic mechanical variations in diverse liver conditions. Our analysis of multiscale viscoelastic disparities through a self-similar hierarchical theoretical framework enhances our understanding of fibrosis evolution. Distinct mechanical signatures observed across liver states provide valuable insights for assessing fibrotic individuals and treatment responses at different spatial scales. Furthermore, we propose a series of threshold values for each marker in the diagnosis of liver fibrosis. Notably, based on these new viscoelastic signatures, we eventually propose a Light Gradient Boosting Machine (LightGBM) diagnostic model that outperforms conventional stiffness-based classification, offering superior diagnostic precision for fibrotic treatment. This research contributes to the growing knowledge of viscoelastic characteristics in soft tissues and holds promise for innovative diagnostic strategies in various diseases and cancers.

Beyond stiffness: Multiscale viscoelastic features as biomechanical markers for assessing cell types and states

Cell mechanics are pivotal in regulating cellular activities, diseases progression, and cancer development. However, the understanding of how cellular viscoelastic properties vary in physiological and pathological stimuli remains scarce. Here, we develop a hybrid self-similar hierarchical theory-microrheology approach to accurately and efficiently characterize cellular viscoelasticity. Focusing on two key cell types associated with livers fibrosis—the capillarized liver sinusoidal endothelial cells and activated hepatic stellate cells—we uncover a universal two-stage power-law rheology characterized by two distinct exponents, αshort and αlong. The mechanical profiles derived from both exponents exhibit significant potential for discriminating among diverse cells. This finding suggests a potential common dynamic creep characteristic across biological systems, extending our earlier observations in soft tissues. Using a tailored hierarchical model for cellular mechanical structures, we discern significant variations in the viscoelastic properties and their distribution profiles across different cell types and states from the cytoplasm (elastic stiffness E1 and viscosity η), to a single cytoskeleton fiber (elastic stiffness E2), and then to the cell level (transverse expansion stiffness E3). Importantly, we construct a logistic-regression-based machine-learning model using the dynamic parameters that outperforms conventional cell-stiffness-based classifiers in assessing cell states, achieving an area under the curve of 97% vs. 78%. Our findings not only advance a robust framework for monitoring intricate cell dynamics but also highlight the crucial role of cellular viscoelasticity in discerning cell states across a spectrum of liver diseases and prognosis, offering new avenues for developing diagnostic and therapeutic strategies based on cellular viscoelasticity.

Computational analysis of power-law fluids for convective heat transfer in permeable enclosures using Darcy effects

Natural convection is a complex environmental phenomenon that typically occurs in engineering settings in porous structures. Shear thinning or shear thickening fluids are characteristics of power-law fluids, which are non-Newtonian in nature and find wide-ranging uses in various industrial processes. Non-Newtonian fluid flow in porous media is a difficult problem with important consequences for energy systems and heat transfer. In this paper, convective heat transmission in permeable enclosures will be thoroughly examined. The main goal is to comprehend the intricate interaction between the buoyancy-induced convection intensity, the porosity of the casing, and the fluid’s power-law rheology as indicated by the Rayleigh number. The objective is to comprehend the underlying mechanisms and identify the ideal conditions for improving heat transfer processes.The problem’s governing equations for a scientific investigation are predicated on the concepts of heat transport and fluid dynamics. The fluid flow and thermal behavior are represented using the energy equation, the Boussinesq approximation, and the Navier–Stokes equations. The continuity equation in a porous media represents the conservation of mass. Finite Element Analysis is the numerical method that is suggested for this challenging topic since it enables a comprehensive examination of the situation. The results of the investigation support several important conclusions. The power-law index directly impacts heat transmission patterns. A higher Rayleigh number indicates increased buoyancy-induced convection, which increases the heat transfer rates inside the shell. The porosity of the medium significantly affects temperature gradients and flow distribution, and it is most noticeable when permeability is present. The findings show how, in the context of porous media, these parameters have complicated relationships with one another.

A generalized method aiming at predicting the polymer melt flow field in the metering zone of large-scale single-screw extruders

Single-screw extruders (SSE) are commonly used in a wide variety of applications, ranging from polymer-extrusion to pellet additive manufacturing (PAM). Existing mathematical models focus on Newtonian and power-law rheologies to model melt flow in the last screw vanes. However, molten polymers usually follow more complex rheological patterns, and a generalized extrusion model is still lacking. Therefore, a semi-analytical model aiming at describing the flow of molten polymers in SSE is presented, to encompass a wide range of non-Newtonian fluids, including generalized non-Newtonian fluids (GNF). The aim is to evaluate the molten polymer flow field under the minimum set of dimensionless parameters. The effect of dimensionless extrusion temperature, flow rate, channel width, and height on the flow field has been investigated. A full factorial plane has been chosen, and it was found that the impact of dimensionless flow rate is the most prominent. The results were initially compared to numerical computations, revealing a strong agreement between the simulations and the proposed GNF method. However, significant deviations emerged when employing the traditional power-law model. This is particularly true at high values of flow rate and extrusion temperature: the mean error on overall flow speed is reduced from 12.91% (traditional power-law method) to 1.04% (proposed GNF method), while keeping a reasonable computational time (time reduction: 96.70%, if compared to fully numerical solutions). Then, the predicted pressure drop in the metering section was benchmarked against established literature data for industrial-scale extruders, to show the model’s accuracy and reliability. The relative errors of the traditional model range between 34.33 and 62%. The proposed method reduces this gap (errors ranging between 5.34% and 10.97%). The low computational time and high accuracy of the GNF method will pave the way for its integration in more complex mathematical models of large-scale additive manufacturing processes.

Soft glassy rheology of single cells with pathogenic protein aggregates.

A correlation between the mechanical properties of cells and various diseases has been emerging in recent years. Atomic force microscopy (AFM) has been widely used to measure a single cell's apparent Young's modulus by treating it as a fully elastic object. More recently, quantitative characterization of the complete viscoelasticity of single cells has become possible. We performed AFM-based nano-indentation experiments on hemocytes isolated from third instar larvae to determine their viscoelasticity and found that live hemocytes, like many other cells, follow a scale-free power-law rheology (PLR) akin to soft glasses. Further, we examined the changes in the rheological response of hemocytes in the presence of pathogenic protein aggregates known to cause neurodegenerative diseases such as Huntington's disorder and amyotrophic lateral sclerosis. Our results show that cells lose their fluidity and appear more solid-like in the presence of certain aggregates, in a manner correlated to actin reorganization. More solid-like cells also display reduced intracellular transport through clathrin-mediated endocytosis (CME). However, the cell's rheology remains largely unaffected and is similar to that of wild-type (WT) hemocytes, if aggregates do not perturb the actin organization and CME. Moreover, the fluid-like nature was significantly recovered when actin organization was rescued by overexpressing specific actin interacting proteins or chaperones. Our study, for the first time, underscores a direct correlation between parameters governing glassy dynamics, actin organization and CME.

Investigation of ultrasound-assisted starch acetylation by single- and dual- frequency ultrasound based on rheology modelling, non-isothermal reaction kinetics, and flow/acoustic simulation

To achieve wheat starch acetylation (AC) with a high degree of substitution (DS), the acetylation process was carried out using various ultrasonication frequencies, including 25 kHz, 40 kHz, and 25 + 40 kHz. In the second step, wheat starch's ultrasound-assisted acetylation (UAA) is simulated using various approaches including the rheology models, non-isothermal reaction kinetics, and flow/acoustic modelling. The computational fluid dynamics (CFD) simulation solves the non-linear acoustic governing equation to determine the flow field and the amount of delivered ultrasound energy. The acetylated starch increased peak and final viscosity, with the highest values observed for the 25 + 40 kHz frequency than other single frequencies (25 kHz and 40 kHz). The viscosity of the starch is specified based on the experimental data using Herschel–Bulkley, power law, and Casson rheology models. According to differential scanning calorimetry (DSC) analysis, the gelatinization parameters and enthalpy of gelatinization (ΔHgel), were found to be lower in acetylated starches at the frequency of 25 + 40 kHz compared to those at frequencies of 25 kHz and 40 kHz, as well as native starches (NS). Moreover, the gelatinization process is examined by implementing the non-isothermal reaction kinetics to obtain the activation energy and reaction order. Based on the results obtained, implementing sonication at 25 kHz reduces the activation energy by 70.3 % compared to native starch. However, the same parameter is obtained to be 69.9 % and 67.1 % for the application of 40 and 25 + 40 kHz transducers, respectively. Additionally, during the sonication treatment, the yield shear stress increases between 24.1 and 31.8 %, based on the applied frequency. Morphology analysis determined by scanning electron microscopy (SEM) revealed that the surfaces and small granules underwent more damage in acetylated starches at frequencies of 25 kHz and 40 kHz. However, in acetylated starches at 25 + 40 kHz, the larger granules were more affected than the smaller ones.

Topological mechanism in the nonlinear power-law relaxation of cell cortex.

Different types of cells exhibit a universal power-law rheology, but the mechanism underneath is still unclear. Based on the exponential distribution of actin filament length, we treat the cell cortex as a collection of chains of crosslinkers with exponentially distributed binding energy, and show that the power-law exponent of its stress relaxation should scale with the chain length. Through this model, we are able to explain how the exponent can be regulated by the crosslinker number and imposed strain during cortex relaxation. Network statistics show that the average length of filament-crosslinker chains decreases with the crosslinker number, which endows a denser network with lower exponent. Due to gradual molecular alignment with the stretch direction, the number of effectively stretched crosslinkers in the network is found to increase with the imposed strain. This effective growth in network density diminishes the exponent under large strain. By incorporating the inclined angle of crosslinkers into the model without in-series structure, we show that the exponent cannot be altered by crosslinker rotation directly, refining our previous conjectures. This work may help to understand cellular mechanics from the molecular perspective.

A life off the beaten track in biomechanics: Imperfect elasticity, cytoskeletal glassiness, and epithelial unjamming.

Textbook descriptions of elasticity, viscosity, and viscoelasticity fail to account for certain mechanical behaviors that typify soft living matter. Here, we consider three examples. First, strong empirical evidence suggests that within lung parenchymal tissues, the frictional stresses expressed at the microscale are fundamentally not of viscous origin. Second, the cytoskeleton (CSK) of the airway smooth muscle cell, as well as that of all eukaryotic cells, is more solid-like than fluid-like, yet its elastic modulus is softer than the softest of soft rubbers by a factor of 104-105. Moreover, the eukaryotic CSK expresses power law rheology, innate malleability, and fluidization when sheared. For these reasons, taken together, the CSK of the living eukaryotic cell is reminiscent of the class of materials called soft glasses, thus likening it to inert materials such as clays, pastes slurries, emulsions, and foams. Third, the cellular collective comprising a confluent epithelial layer can become solid-like and jammed, fluid-like and unjammed, or something in between. Esoteric though each may seem, these discoveries are consequential insofar as they impact our understanding of bronchospasm and wound healing as well as cancer cell invasion and embryonic development. Moreover, there are reasons to suspect that certain of these phenomena first arose in the early protist as a result of evolutionary pressures exerted by the primordial microenvironment. We have hypothesized, further, that each then became passed down virtually unchanged to the present day as a conserved core process. These topics are addressed here not only because they are interesting but also because they track the journey of one laboratory along a path less traveled by.

Fast relocking and afterslip-seismicity evolution following the 2015 Mw 8.3 Illapel earthquake in Chile

Large subduction earthquakes induce complex postseismic deformation, primarily driven by afterslip and viscoelastic relaxation, in addition to interplate relocking processes. However, these signals are intricately intertwined, posing challenges in determining the timing and nature of relocking. Here, we use six years of continuous GNSS measurements (2015–2021) to study the spatiotemporal evolution of afterslip, seismicity and locking after the 2015 Illapel earthquake (M_w 8.3). Afterslip is inverted from postseismic displacements corrected for nonlinear viscoelastic relaxation modeled using a power-law rheology, and the distribution of locking is obtained from the linear trend of GNSS stations. Our results show that afterslip is mainly concentrated in two zones surrounding the region of largest coseismic slip. The accumulated afterslip (corresponding to M_w 7.8) exceeds 1.5 m, with aftershocks mainly occurring at the boundaries of the afterslip patches. Our results reveal that the region experiencing the largest coseismic slip undergoes rapid relocking, exhibiting the behavior of a persistent velocity weakening asperity, with no observed aftershocks or afterslip within this region during the observed period. The rapid relocking of this asperity may explain the almost regular recurrence time of earthquakes in this region, as similar events occurred in 1880 and 1943.

Pore-scale hydrodynamics of non-Newtonian power-law fluids across a partially blocked porous medium in a confined channel

Transport of non-Newtonian fluids in porous media is pervasive in many natural and industrial applications. However, capturing the rheological behaviors of fluids by direct experimental techniques is challenging at the pore-scale. This paper outlines the pore-scale hydrodynamic interactions of non-Newtonian power-law fluids across a partially blocked porous medium in the laminar flow regime by computational fluid dynamics. The porous medium consists of an array of uniformly arranged square pillars. We explore the complex interplay of power-law rheology and Reynolds number on the microscopic flow field at the pore-scale. We capture the momentum transfer at the permeable interface between the porous and non-porous regions through stream-wise and span-wise velocity components and average volumetric flow rates at each pore-throat. Our results unveil a significant augmentation in stream-wise momentum by shear-thinning behavior and a diminution in momentum by shear-thickening behavior of the fluid through the porous medium. Further, the flow-leakage at the top interface purely depends on the combined effects of Reynolds number and power-law index. The channel pressure drop between the windward and leeward faces of the porous medium increases with the power-law index at low Reynolds number, while it decreases at high Reynolds number. Moreover, we provide a simple numerical framework to comprehend how the power-law behavior of the fluid dynamically regulates the flow field at the pore-scale.

Strain-Controlled Critical Slowing Down in the Rheology of Disordered Networks.

Networks and dense suspensions frequently reside near a boundary between soft (or fluidlike) and rigid (or solidlike) regimes. Transitions between these regimes can be driven by changes in structure, density, or applied stress or strain. In general, near the onset or loss of rigidity in these systems, dissipation-limiting heterogeneous nonaffine rearrangements dominate the macroscopic viscoelastic response, giving rise to diverging relaxation times and power-law rheology. Here, we describe a simple quantitative relationship between nonaffinity and the excess viscosity. We test this nonaffinity-viscosity relationship computationally and demonstrate its rheological consequences in simulations of strained filament networks and dense suspensions. We also predict critical signatures in the rheology of semiflexible and stiff biopolymer networks near the strain stiffening transition.

Viscoelastic Multiscale Mechanical Indexes for Assessing Liver Fibrosis and Treatment Outcomes.

Understanding liver tissue mechanics, particularly in the context of liver pathologies like fibrosis, cirrhosis, and carcinoma, holds pivotal significance for assessing disease severity and prognosis. Although the static mechanical properties of livers have been gradually studied, the intricacies of their dynamic mechanics remain enigmatic. Here, we characterize the dynamic creep responses of healthy, fibrotic, and mesenchymal stem cells (MSCs)-treated fibrotic lives. Strikingly, we unearth a ubiquitous two-stage power-law rheology of livers across different time scales with the exponents and their distribution profiles highly correlated to liver status. Moreover, our self-similar hierarchical theory effectively captures the delicate changes in the dynamical mechanics of livers. Notably, the viscoelastic multiscale mechanical indexes (i.e., power-law exponents and elastic stiffnesses of different hierarchies) and their distribution characteristics prominently vary with liver fibrosis and MSCs therapy. This study unveils the viscoelastic characteristics of livers and underscores the potential of proposed mechanical criteria for assessing disease evolution and prognosis.

A deformability-based biochip for precise label-free stratification of metastatic subtypes using deep learning

Cellular deformability is a promising biomarker for evaluating the physiological state of cells in medical applications. Microfluidics has emerged as a powerful technique for measuring cellular deformability. However, existing microfluidic-based assays for measuring cellular deformability rely heavily on image analysis, which can limit their scalability for high-throughput applications. Here, we develop a parallel constriction-based microfluidic flow cytometry device and an integrated computational framework (ATMQcD). The ATMQcD framework includes automatic training set generation, multiple object tracking, segmentation, and cellular deformability quantification. The system was validated using cancer cell lines of varying metastatic potential, achieving a classification accuracy of 92.4% for invasiveness assessment and stratifying cancer cells before and after hypoxia treatment. The ATMQcD system also demonstrated excellent performance in distinguishing cancer cells from leukocytes (accuracy = 89.5%). We developed a mechanical model based on power-law rheology to quantify stiffness, which was fitted with measured data directly. The model evaluated metastatic potentials for multiple cancer types and mixed cell populations, even under real-world clinical conditions. Our study presents a highly robust and transferable computational framework for multiobject tracking and deformation measurement tasks in microfluidics. We believe that this platform has the potential to pave the way for high-throughput analysis in clinical applications, providing a powerful tool for evaluating cellular deformability and assessing the physiological state of cells.

Post-seismic gravity change modelling based on non-linear power-law upper mantle rheology

SUMMARY Post-seismic gravity change modelling is commonly based on earth model with Newtonian linear rheology. Here, we present a novel way of modelling post-seismic gravity change by using a non-linear power-law rheology earth model. The method is constructed based on the framework of spectral finite element method (SFEM). SFEM has been proven practical for the purpose of modelling gravity change occurring during megathrust earthquakes. Our method implements the strain rate expression of non-linear power-law rheology into the mathematical framework of SFEM. Using our method, simulations of geoid change caused by synthetic point source earthquakes were made. The results revealed the potential of using non-linear power-law rheology for the explanation of rapid gravity changes in the beginning of the post-seismic epoch. Further on, we computed the post-seismic gravity change of the 2011 M9.0 Tohoku-Oki earthquake based on Maxwell non-linear power-law rheology in the upper mantle. It demonstrated the potential of power-law upper mantle flow as a possible candidate for the explanation of post-seismic gravity change after the earthquake occurs. However, a Maxwell non-linear power-law rheology alone is insufficient for the explanation of the post-seismic gravity change occurred.

Grain size reduction by plug flow in the wet oceanic upper mantle explains the asthenosphere's low seismic Q zone

The prominent seismic low-velocity zone (LVZ) in the oceanic low-viscosity asthenosphere is approximately coincident with the low seismic Q zone (LQZ; a zone of high seismic attenuation). Small olivine grain sizes could link these seismic and rheological properties because they reduce viscosity, seismic velocity and seismic Q. Because rock deformation reduces grain sizes, the asthenosphere's seismic properties can place constraints on asthenospheric flow. To determine dominant flow patterns, we develop a self-consistent analytical 1-D channel flow model that accounts for upper mantle rheology and its dependence on flow-modified grain-sizes, water content, and melt fraction, for flow driven by both surface plate motions (Couette flow) and/or horizontal pressure gradients (Poiseuille flow). We find that Couette flow dominates if the upper mantle is dry, and plug flow (a Poiseuille flow for power law rheology) dominates if it is weakened by wet conditions. A plug flow configuration spanning the upper 670 km of the mantle best explains the LQZ in the asthenosphere, and can be attributed to significant grain-size reduction due to extensive shearing across the asthenosphere. This flow configuration also explains high seismic Q values below the asthenosphere associated with minimal shear deformation and large grain sizes above the mantle transition zone. We suggest that the asthenospheric LQZ and LVZ seismic anomalies can be largely explained by grain-size variations associated with plug flow in the wet upper mantle.