Viscoelastic Relaxation Research Articles

Collective dynamics of liquid acetone investigated by inelastic X-ray scattering

The dynamic structure factors S(Q,ω) of liquid acetone were measured in a wide Q range 1.9–41.2 nm−1 with a high-resolution inelastic X-ray scattering (IXS) spectrometer installed at BL35XU of the SPring-8. Highly damped collective excitations of the longitudinal acoustic (LA) phonons are observed. The IXS spectra were analyzed by using a generalized Langevin formalism with the help of a sparse modeling to deduce reasonable Q dependences of the fitting parameters. The dispersion relation of the LA phonon excitations shows a highly positive deviation by about 65% from the adiabatic velocity of sound, which is larger than that in non-polar liquids such as CCl4 and benzene with van der Waals interactions, due probably that the acetone is a polar liquid. Microscopic dynamic parameters, such as viscoelastic relaxation rates and viscosity, are discussed by comparing with existing macroscopic dynamic properties. The fast and slow viscoelastic relaxations correspond to the vibration dynamics and reorientation correlations, respectively.

Overlapped Postseismic Deformation Caused by Afterslip and Viscoelastic Relaxation Following the 2015 Mw 7.8 Gorkha (Nepal) Earthquake

AbstractStudying transient postseismic deformation is one of the key approaches to probe fault kinematics and rheological behavior of rocks surrounding tectonic faults. Previous studies have shown that transient postseismic deformation is dominantly induced by afterslip and postseismic viscoelastic relaxation. However, effects of these two mechanisms are generally overlapped in space and time, making the analysis of the observations challenging. Here, we investigate the overlapping effects of afterslip and viscoelastic relaxation following the 2015 Gorkha earthquake based on the first 4‐years’ Global Positioning System observations and finite element models. Separated mechanisms either fail to explain the observations or lead to unreasonable model parameters. A combined model that incorporates stress‐driven afterslip and viscoelastic relaxation can overcome the limitations of separated mechanisms. Our results indicate that only short‐term (<1 year) postseismic deformation in near‐to middle‐fields is caused mainly by afterslip, whereas that in far‐field or long‐term are dominated by the viscoelastic relaxation effect. The stress‐driven afterslip is mainly confined to a narrow zone adjacent to the coseismic rupture asperities, in contrast to the widespread deep afterslip as suggested by previous studies. The total seismic moment released by the afterslip is ∼5% of that released by the Mw 7.8 main shock. The optimal viscosity of the lower crust beneath the south Tibet is estimated to be 2.5 × 1018 Pa∙s, which is at least one order lower than that beneath Indian plate, suggesting a significant lateral variation across the Himalayan fault. Validations by using independent InSAR observations further confirm the reliability of the combined model.

Ground Deformation After a Caldera Collapse: Contributions of Magma Inflow and Viscoelastic Response to the 2015–2018 Deformation Field Around Bárðarbunga, Iceland

AbstractImprovement of our understanding of the role of ground deformation due to viscoelastic relaxation following eruptions is important, as the generated signals can resemble renewed magma inflow. We study post‐eruptive unrest at the subglacial Bárðarbunga volcano, Iceland, after a caldera collapse and major magma drainage in 2014–2015. Elevated seismicity began about 6 months after the eruption ended, including nine Mlw > 4.5 earthquakes. Global Navigation Satellite System and Sentinel‐1 Interferometric Synthetic Aperture Radar geodesy are applied to evaluate post‐eruptive ground deformation from 2015 to 2018. Horizontal velocities locally exceed 10 cm/year and rapidly decay with distance away from the caldera. We explore two end‐member models and their combination to explain the post‐eruptive deformation field: 1) viscoelastic relaxation caused by the co‐eruptive caldera collapse and magma withdrawal, and 2) renewed magma inflow. We find parameter combinations for each model that explain the observed ground deformation. The purely viscoelastic relaxation model, consisting of a half‐space composed of a 7‐km thick elastic layer on top of a viscoelastic layer with a viscosity of 3.0 × 1018 Pa s reproduces broadly the observations. A simple magma inflow model consisting of a single point source with an inflow rate of 1 × 107 m3/year at 0.7 km depth broadly fits the observations, but may be unrealistic. A more elaborate model of magma inflow into a 10‐km deep sill combined with slip on the caldera ring fault explains the observations well. Our results suggest that the co‐eruptive deformation field is likely influenced by viscoelastic relaxation, renewed magma inflow, or a combination of both processes.

Friction Force During Lubricated Steady Sliding of a Rigid Cylinder on a Viscoelastic Substrate

We study the friction force during lubricated sliding of a rigid cylindrical indenter against a viscoelastic substrate in the iso-viscous visco-elasto-hydrodynamic lubrication (VEHL) regime. The substrate is represented by a foundation model. The solution is controlled by three dimensionless parameters. The first of these, λ, measures the time for the indenter to move one contact zone relative to the viscoelastic relaxation time; the second is the ratio of the long time to short time compliance of the substrate, $$c_{\infty } /c_{0}$$ ; the third parameter, β, is the ratio of average fluid flow rate to the sliding velocity. Although our solution works well for the full range of parameters, we focus on the “Hertz” regime (β >>1) where practically all the fluid in the contact region is squeezed out. This regime is quite common in soft contact lubrication problems and presents significant numerical difficulties. Our analysis gives insight into why these numerical difficulties arise. The friction force can be decomposed into two parts, one due to viscoelastic dissipation and the other from hydrodynamics. Although these two are generally coupled, in the Hertz limit, an important result is that the viscoelastic portion of the friction force can be well approximated by the solution of the corresponding “dry” sliding problem, in which there is no lubricating fluid layer. This provides a simple way to decouple the hydrodynamic portion of the friction force from the viscoelasticity of the substrate. We study how hydrodynamic pressure and film thickness vary with the controlling dimensionless parameters. Scaling laws for these relationships are given in closed form.

Static Structure Factor and Viscoelastic Properties of Dendrimer Grafted Nanoparticles in Solution.

The theory for the dynamics of multiscale branched polymeric structures is applied to understand the dendrimer-grafted nanoparticles in a dilute solution. The multiscale nature of dendrimer-grafted nanoparticles arises due to larger beads for the nanoparticles and the smaller beads for the polymeric structure connected through the harmonic springs. The multiscale generalized Gaussian structure approach allows us to study several viscoelastic properties: (i) storage and loss moduli and (ii) intrinsic viscosity. The influence of nanoparticles in the dendrimer structure is reflected in low and intermediate frequency regimes of the viscoelastic relaxation moduli. The increase in the size and the number fraction of nanoparticle shows an anomalous enhancement in the relaxation moduli. The increase in number fraction of nanoparticle in dendrimer-grafted nanoparticles decreases the transition frequency between solid- and liquid-like viscoelastic region. The intrinsic viscosity of dendrimer-grafted nanoparticles increases with increasing the size of nanoparticle. The inclusion of hydrodynamic interactions facilitates the dynamics of dendrimer-grafted nanoparticles. The Kratky plot of the static structure factor of all conformation of dendrimer-grafted nanoparticles is also analyzed as a function of number fraction and the size of the nanoparticles. At low wavenumbers, all conformations of dendrimer-grafted nanoparticles show a universal behavior. The compactness of dendrimer-grafted nanoparticles increases with the increase in number fraction and the size of the nanoparticles.

Astromodal wave dynamics in multifluidic structure-forming cloud complexes

The evolutionary dynamics of bimodal pulsational mode, arising because of the long-range conjugational gravito-electrostatic interplay in viscoelastic polytropic complex multicomponent astroclouds with partial ionisation, is classically examined using a non-relativistic generalised hydrodynamic model approach. The equilibrium distribution of the diversified constitutive species forms a globally quasi-neutral hydrostatic homogeneous configuration. The primitive set of the astrocloud structuring equations specifically includes polytropic (hydrodynamic action) and nonlinear logatropic barotropic (turbulence action) effects simultaneously. A normal mode analysis over the perturbed cloud results in a unique form of sextic polynomial dispersion relation with variable poly-parametric coefficients. A numerical analysis technique is provided to show the exact nature of the modified viscoelastic (turbo-viscoelastic) pulsational mode in the two extreme hydrodynamic and kinetic regimes. It is seen that, in the former regime, the dust–charge ratio (negatively-to-positively charged grains) plays a destabilising role to the instability. In contrast, the dust–mass ratio (negatively-to-positively charged grains) develops a stabilising influence in the wave-dynamical processes. In the latter regime, the viscoelastic relaxation velocity associated with the positively charged grains acts as an amplitude stabiliser. Conversely, the viscoelastic relaxation velocity of the negatively charged grain fluid introduces destabilising influences. The unique features of the propagatory and non-propagatory mode characteristics are elaborately illustrated. The reliability of the investigated results is judiciously validated by comparing the results with the specific reports available in the literature. Lastly, the first-hand astronomical implications and applications of our study are summarily outlined.

Current-Dependent Dynamics of Bidirectional Self-Folding for Multi-Layer Polymers Using Local Resistive Heating

Abstract The purpose of this paper is to characterize the dynamics and direction of self-folding of pre-strained polystyrene (PSPS) and non-pre-strained styrene (NPS), which results from local shrinkage using a new process of directed self-folding of polymer sheets based on a resistively heated ribbon that is in contact with the sheets. A temperature gradient across the thickness of this shape memory polymer (SMP) sheet induces folding along the line of contact with the heating ribbon. Varying the electric current changes the degree of folding and the extent of local material flow. This method can be used to create practical three-dimensional (3D) structures. Sheets of PSPS and NPS were cut to 10 × 20 mm samples, and their folding angles were plotted with respect to time, as obtained from in situ videography. In addition, the use of polyimide tape (Kapton) was investigated for controlling the direction of self-folding. Results show that folding happens on the opposite side of the sample with respect to the tape, regardless of which side the heating ribbon is on, or whether gravity is opposing the folding direction. The results are quantitatively explained using a viscoelastic finite element model capable of describing bidirectional folds arising from the interplay between viscoelastic relaxation and strain mismatch between polystyrene and polyimide. Given the tunability of fold times and the extent of local material flow, resistive-heat-assisted folding is a promising approach for manufacturing complex 3D lightweight structures by origami engineering.

Viscoelastic control of spatiotemporal order in bacterial active matter.

Active matter consists of units that generate mechanical work by consuming energy1. Examples include living systems (such as assemblies of bacteria2-5 and biological tissues6,7), biopolymers driven by molecular motors8-11 and suspensions of synthetic self-propelled particles12-14. A central goal is to understand and control the self-organization of active assemblies in space and time. Most active systems exhibit either spatial order mediated by interactions that coordinate the spatial structure and the motion of active agents12,14,15 or the temporal synchronization of individual oscillatory dynamics2. The simultaneous control of spatial and temporal organization is more challenging and generally requires complex interactions, such as reaction-diffusion hierarchies16 or genetically engineered cellular circuits2. Here we report a simple technique to simultaneously control the spatial and temporal self-organization of bacterial active matter. We confine dense active suspensions of Escherichia coli cells and manipulate a single macroscopic parameter-namely, the viscoelasticity of the suspending fluid- through the addition of purified genomic DNA. This reveals self-driven spatial and temporal organization in the form of a millimetre-scale rotating vortex with periodically oscillating global chirality of tunable frequency, reminiscent of a torsional pendulum. By combining experiments with an active-matter model, we explain this behaviour in terms of the interplay between active forcing and viscoelastic stress relaxation. Our findings provide insight into the influence of bacterial motile behaviour in complex fluids, which may be of interest in health- and ecology-related research, and demonstrate experimentally that rheological properties can be harnessed to control active-matter flows17,18. We envisage that our millimetre-scale, tunable, self-oscillating bacterial vortex may be coupled to actuation systems to act a 'clock generator' capable of providing timing signals for rhythmic locomotion of soft robots and for programmed microfluidic pumping19, for example, by triggering the action of a shift register in soft-robotic logic devices20.

Postseismic Deformation due to the 2012 Mw 7.8 Haida Gwaii and 2013 Mw 7.5 Craig Earthquakes and its Implications for Regional Rheological Structure

AbstractObservations of ∼7 years of postseismic deformation following the 2012 M w 7.8 Haida Gwaii and 2013 M w 7.5 Craig earthquakes in western British Columbia and southeastern Alaska provides insight into the regional rheologic structure and seismological hazards. A stress‐driven afterslip‐only model cannot alone explain rates or spatial patterns of the far field and later stage postseismic deformation measured by Global Positioning System (GPS). We thus develop an integrated model that fits the observations by combining afterslip on the deeper extension of the faults and distributed viscous flow in the asthenosphere. The best‐fit integrated model has a 60‐km thick lithosphere overlying a Burgers body asthenosphere with a Maxwell viscosity of 2 × 1019 Pa s (0.8–3 × 1019 Pa s at 95% confidence), with a Kelvin viscosity assumed equal to 10% of that value. These values are in good agreement with rheological models derived from glacial isostatic adjustment data. The early, near‐field postseismic deformation from both events is dominated by their corresponding afterslip, however, throughout the Craig postseismic period, the dominant mechanism in the far field is viscoelastic relaxation. For the intermediate region between the two earthquakes, both events contribute to the observed postseismic displacements. Because there was no obvious afterslip following the Haida Gwaii event or known large historical earthquakes on the southernmost part of the QCF, this region continues to have great potential to suffer a large earthquake in the future.

Investigating the Influences of Crustal Thickness and Temperature on the Uplift of Mantle Materials Beneath Large Impact Craters on the Moon

AbstractIn this work, we examine variations in the mantle uplift associated with large lunar impact craters and basins between major terranes. This study is based on Bouguer gravity anomalies of 100–650‐km diameter impact craters using Gravity Recovery and Interior Laboratory (GRAIL) observations and the Lunar Orbiter Laser Altimeter (LOLA) crater database. The Bouguer gravity anomalies of 324 large impact craters analyzed herein are primarily controlled by the uplifted crust‐mantle (Moho) interface in the central region of these impact craters, while postimpact mare deposits that represent ∼25%–35% of the postimpact deposit column also contribute to the gravity anomalies of mare craters. The central uplift of the Moho interface is primarily controlled by impact energy and increases to ∼ 30 km for a 650‐km diameter crater. Analyses of nonmare craters in the Feldspathic Highlands Terrane (FHT) with varied crustal thickness (Tc) reveal that the onset crater diameter (Dmin) with an uplifted Moho interface is dependent on the local Tc: Dmin ∼ 150 + 1.3Tc (in a unit of km). This equation also provides a quantification of the depth‐dependent attenuation of impact‐induced structural uplift, using the Moho uplift as a proxy for the structural uplift. The Moho uplift of large craters in the South Pole‐Aitken (SPA) Terrane is not statistically different from the FHT craters, consistent with limited overall thermal difference between these two terranes and compensational thermal effects at crater collapse and viscoelastic relaxation stages.

A novel assessment of microstructural and mechanical behaviour of bilayer silica-reinforced nanocomposite hydrogels as a candidate for artificial cartilage

The complex structure of healthy articular cartilage facilitates the joint withstanding the imposed pressures and retaining interstitial fluid to lessen stresses on its soft tissue, while easing the locomotion and minimising friction between cartilage mates. Avascular nature of this tissue results in unrecoverable damaged lesions and severe pain over time. Polymeric hydrogels are promising candidate materials for the replacement of the damaged cartilage. Hence, a tough bilayer nanocomposite acrylamide-acrylic acid hydrogel reinforced with silica nanoparticles (SNPs) was designed and synthesised. The mechanical characterisations showed a significant increase in compressive strength up to 1.4 MPa and doubled elastic modulus (240 kPa) by utilising only 0.6 wt% SNPs compared to the non-reinforced hydrogel. The optimum amounts of monomers and SNPs resulted in the compression of samples up to 85% strain without failure. Viscoelastic responses improved as the stress relaxation lessened to half in all nanocomposite hydrogels. Diffusion rate theory was applied, and the results showed to what extent elastic modulus results in an improvement in stress relaxation. The proposed hydrogel formulation exhibited the poroelastic relaxation occurred before viscoelastic relaxation at the time elapses under stress relaxation tests. SEM images showed uniform funnel-like porosity with 570 μm thick lubricious layer, which is an important feature to retain interstitial fluid. Energy-dispersive X-ray spectroscopy was conducted to characterise the elemental composition within the polymeric macrostructure.

Frequency Dependence of Nonlinear Viscoelastic Relaxation in Glassy Epoxy Network Subjected to Constant-Speed Stretching

Frequency Dependence of Nonlinear Viscoelastic Relaxation in Glassy Epoxy Network Subjected to Constant-Speed Stretching

Model studies of advanced glycation end product modification of heterograft biomaterials: The effects of in vitro glucose, glyoxal, and serum albumin on collagen structure and mechanical properties

Glutaraldehyde cross-linked heterograft tissues, bovine pericardium (BP) or porcine aortic valves, are the leaflet materials in bioprosthetic heart valves (BHV) used in cardiac surgery for heart valve disease. BHV fail due to structural valve degeneration (SVD), often with calcification. Advanced glycation end products (AGE) are post-translational, non-enzymatic reaction products from sugars reducing proteins. AGE are present in SVD-BHV clinical explants and are not detectable in un-implanted BHV. Prior studies modeled BP-AGE formation in vitro with glyoxal, a glucose breakdown product, and serum albumin. However, glucose is the most abundant AGE precursor. Thus, the present studies investigated the hypothesis that BHV susceptibility to glucose related AGE, together with serum proteins, results in deterioration of collagen structure and mechanical properties. In vitro experiments studied AGE formation in BP and porcine collagen sponges (CS) comparing 14C-glucose and 14C-glyoxal with and without bovine serum albumin (BSA). Glucose incorporation occurred at a significantly lower level than glyoxal (p<0.02). BSA co-incubations demonstrated reduced glyoxal and glucose uptake by both BP and CS. BSA incubation caused a significant increase in BP mass, enhanced by glyoxal co-incubation. Two-photon microscopy of BP showed BSA induced disruption of collagen structure that was more severe with glucose or glyoxal co-incubation. Uniaxial testing of CS demonstrated that glucose or glyoxal together with BSA compared to controls, caused accelerated deterioration of viscoelastic relaxation, and increased stiffness over a 28-day time course. In conclusion, glucose, glyoxal and BSA uniquely contribute to AGE-mediated disruption of heterograft collagen structure and deterioration of mechanical properties.

Varying least principal stress along lithofacies in gas shale reservoirs: effects of frictional strength and viscoelastic stress relaxation

Compositional variation of rock properties in unconventional shale reservoirs impacts not only hydraulic fracturing stimulation but also the variability of induced shear slip on pre-existing fracture networks. Lithological layering is also responsible for varying stress states in various unconventional reservoirs subjected to normal, strike-slip, reverse or hybrid faulting regime (a combination of any two of them). Three possible mechanisms are considered to evaluate the layer-based stress profile in the sub-surface, that is viscoelastic stress relaxation, elevated pore pressure and variation in rock frictional strength. We conducted multistage triaxial deformation tests with varying strain rates (5×10−7 to 10−5s−1) on shale sample originating from three lithological units of the Goldwyer shale formation, that is G-I, G-II and G-III in the Broome platform of onshore Canning basin. Additionally, pore pressure was estimated from wireline logs, and tectonic stress accumulation was modelled using time-dependent deformation (creep) data. The above analysis suggests that varying frictional strength alone could not explain the variation of the least principal stress; however, the inclusion of stress relaxation also contributes, whereas elevated pore pressure has no effect. Using this approach, we could also relate the changes in minimum principal stress (Shmin) from one lithofacies to the other and anticipate how this will impact the optimum design of landing zone during horizontal drilling and completion in unconventional field development.

Viscoelastic relaxation of the upper mantle and afterslip following the 2014 MW8.1 Iquique earthquake

An improved understanding of postseismic crustal deformation following large subduction earthquakes may help to better understand the rheological properties of upper mantle and the slip behavior of subduction interface. Here we construct a three-dimensional viscoelastic finite element model to study the postseismic deformation of the 2014 MW8.1 Iquique, Chile earthquake. Elastic units in the model include the subducting slab, continental and oceanic lithospheres. Rheological units include the mantle wedge, the oceanic asthenosphere and upper mantle. We use a 2 ​km thick weak shear zone attached to the subduction fault to simulate the time-dependent stress-driven afterslip. The viscoelastic relaxation in the rheological units is represented by the Burgers rheology. We carry out grid-searches on the shear zone viscosity, thickness and viscosity of the asthenosphere, and they are determined to be 1017 ​Pa ​s, 110 ​km and 2 ​× ​1018 ​Pa ​s, respectively. The stress-driven afterlsip within the first two years is up to ~47 ​cm and becomes negligible after two years (no more than 5 ​cm/yr). Our results suggest that a thin, low-viscosity oceanic asthenosphere together with a weak shear zone attached to the fault are required to better reproduce the observed postseismic deformation.

Revealing viscoelastic bending relaxation dynamics of isolated semiflexible colloidal polymers.

The viscoelastic properties of filaments and biopolymers play a crucial role in soft and biological materials from biopolymer networks to novel synthetic metamaterials. Colloidal particles with specific valency allow mimicking polymers and more complex molecular structures at the colloidal scale, offering direct observation of their internal degrees of freedom. Here, we elucidate the time-dependent viscoelastic response in the bending of isolated semi-flexible colloidal polymers, assembled from dipatch colloidal particles by reversible critical Casimir forces. By tuning the patch-patch interaction strength, we adjust the polymers' viscoelastic properties, and follow spontaneous bending modes and their relaxation directly on the particle level. We find that the elastic response is well described by that of a semiflexible rod with persistence length of order 1000 μm, tunable by the critical Casimir interaction strength. We identify the viscous relaxation on longer timescales to be due to internal friction, leading to a wavelength-independent relaxation time similar to single biopolymers, but in the colloidal case arising from the contact mechanics of the bonded patches. These tunable mechanical properties of assembled colloidal filaments open the door to "colloidal architectures", rationally designed (network) structures with desired topology and mechanical properties.

Electro-viscoelasticity of agarose based electrorheological fluids

In this article, we report a new class of colloidal, micrometer-scale agarose powder based organic electrorheological (ER) fluids and its ER and viscoelastic characteristics. The steady shear ER characteristic of the colloids shows enhancements in the yield stress of the fluid, and yield stress values approaching ∼1 kPa have been noted. The ER hysteresis and electro-thixotropy illustrate that the microstructure of the colloids under field effects is able to withstand dynamic and impact stresses with good repeatability. The electro-creep strain and stress relaxation characteristics of the colloids show transition to the elastoviscous state with an increase in electric field strength. The oscillatory shear ER characteristic of the colloids shows field induced transition from a fluid-like nature to solid-like nature. Atypical regimes of loss and regain in viscoelastic nature are noted for the colloids under different field constraints. The viscoelastic dissipation and complex viscosity characteristics are also discussed for utilitarian aspects. Mathematical analysis reveals that the electric field induced viscoelastic, creep strain, and stress relaxation signatures of the colloids conform to fractional derivative elastoviscous models. The present findings may find significant implications toward the design and development of organic particle based ER fluids.

Viscoelastic Relaxation of the Nuclear Envelope Does Not Cause the Collapse of the Spindle After Ablation in S. pombe.

A large molecular machine called the mitotic spindle is responsible for accurate chromosome segregation in eukaryotic cells. The spindle consists of protein filaments known as microtubules and microtubule-associated proteins such as motors and crosslinkers, which help impart its organization. In the case of the fission yeast S. pombe, these form a single bundle inside the nucleus. During spindle elongation, sliding by motor proteins provides an internal source of extensile forces, which are resisted by the compressive forces of the nuclear envelope. To probe the sources of this force balance, we cut the spindle using focused laser light at various stages of spindle elongation. We find that the spindle pole bodies collapse toward each other post-ablation. While this basic behavior has been previously observed, many questions remain about the timing, mechanics, and molecular requirements of this phenomenon. Here, we quantify the time scale of the relaxation and probe its underlying mechanism. We demonstrate that viscoelastic relaxation of the nuclear envelope cannot explain this phenomenon and provide evidence of active forces as the underlying mechanism.

DYNAMIC COUPLED THERMO-HYDRO-MECHANICAL PROBLEM FOR SATURATED POROUS VISCOELASTIC FOUNDATION

Natural soil often has the characteristics of rheology due to different depositional conditions and stress states. The present paper focuses on investigated the effects of different porosity and permeability coefficient in saturated porous foundation which considered the viscoelastic relaxation times with coupled thermo-hydro-mechanical fields under external load. A two-dimensional coupled thermo-hydro-mechanical dynamics problem for a half-space on an isotropic, uniform, fully saturated, and poroviscoelastic soil (THMVD) whose surface is subjected to either mechanical force or thermal load based on the Biot's wave theory of porous media, Darcy's law, and Lord-Shulman (L-S) generalized thermoelastic theory with Kelvin-Voigt viscoelastic model is investigated. The general relationships among the non-dimensional vertical displacement, excess pore water pressure, vertical stress, and temperature distribution are then deduced via normal mode analysis and depicted graphically. Normal mode analysis is a method using weighted residuals to derive analytical solutions. Via this method, the equation can be divided into two parts without integral transformation and inverse transformation, thereby increasing the speed of decoupling and eliminating the limitation of numerical inverse transformation. The effects of the porosity and the permeability coefficient on the four different physical variables have been investigated. It can be shown that: whatever load is being considered, the variation of load frequencies have obvious effect on all the considered physical variables; the porosity and permeability have the most obvious influence on non-dimension excess pore water pressure. When thermal loads were considered only, the variation of porosity and permeability coefficient had barly effect on non-dimension temperature. This proposed derivation method can be widely applied in the geotechnical engineering field, especially with regard to the mechanical and thermal behaviors of commercial buildings, high-speed railways, and highway energy foundations. The research results of this problem can lay a certain theoretical foundation for engineering construction and have a certain guiding significance.

Weakly nonlinear interactions of collective oscillations in a correlated degenerate fluid

A generalized viscoelastic quantum hydrodynamic model is proposed for the dynamics of strongly correlated degenerate isothermal fluid. The quantum forces associated with the quantum diffraction effect along with the strong correlation effects are embedded in this transport equation through the viscoelastic relaxation of correlations. The collective dynamics of linear and nonlinear modes in such correlated degenerate fluid are also investigated. In the high-frequency oscillation (kinetic regime), the dynamics of the weakly nonlinear mode is found to be governed by a novel equation with a memory dependent non-local nonlinear term that describes the strong correlation effect. This novel equation is solved analytically and numerically. In the low-frequency oscillation (hydrodynamic regime), the weakly nonlinear mode is found to be governed by a Korteweg–de Vries Burgers' equation that exhibits dispersive shock wave. In both the dynamics, quantum diffraction introduces the dispersive effect.