Viscous Model Research Articles

How external photoevaporation changes the chemical composition of the inner disc

Stars mostly form in cluster environments, where neighbouring stars can have an influence on the evolution of the newly formed protoplanetary discs. Besides gravitational interactions, external photoevaporation can also shape protoplanetary discs. Depending on the strength of external photo-evaporation, discs may be destroyed within 1–2 Myrs, or more gradually, depending on whether the external photo-evaporation field is stronger or weaker, respectively. We used the chemcomp code, which includes a viscous disc evolution model including pebble drift and evaporation to calculate the chemical composition of protoplanetary discs. We extended this code to include external photoevaporation following the FRIED grid. Before external photoevaporation becomes efficient, the disc follows a purely viscous disc evolution, where the C/O ratio in the inner disc initially decreases due to inwardly drifting and evaporating water ice pebbles. Over time, the C/O ratio increases again as water vapour is accreted onto the star and carbon-rich gas gradually migrates inwards. However, once external photo-evaporation commences, the outer disc begins to get dispersed. During this process, the inner disc’s chemical evolution still follows the evolution of a purely viscous disc because the majority of the pebbles have already drifted inwards on timescales shorter than 1 Myr. At low viscosity, the inner disc’s C/O ratio remains sub-solar until the disc is dispersed through external photoevaporation. At a high viscosity, the inner disc’s composition can reach super-solar values in C/O, because the water vapour is accreted onto the star faster and carbon rich gas from the outer disc can move inwards faster as well, as long as the disc can survive a few Myrs. In both cases, there is no visible difference in terms of the chemical composition of the inner disc compared to a purely viscous model, due to the rapid inward drift of pebbles that sets the chemical composition of the disc. Thus, our model predicts that the inner disc chemistry would be similar between discs that are subject to external photoevaporation and discs that are isolated and experience no external photo-evaporation. This finding is in line with observations of protoplanetary discs with JWST.

A comparative study of low cyclic loading effects on plastic strain, nonlinear damping, and strength softening in fiber-reinforced recycled aggregate concrete

The incorporation of fibers significantly enhances the properties and structural performance of recycled aggregate concrete. This study introduces Fiber-Reinforced Recycled Aggregate Concrete (FRAC) by integrating steel fibers (SF) and polypropylene fibers (PPF) into the recycled aggregate concrete (RAC) matrix. A comprehensive series of cyclic loading tests, including reload and unload sequences, were conducted to meticulously analyze the deterioration of strength and energy dissipation capabilities of SF/PPF-reinforced RAC. The research examines the effects of fiber characteristics, volume ratios, lengths, and diameters on strength degradation after the peak stress along the stress-strain curve. Degradation models based on plastic strain were proposed for both SF-reinforced RAC and PPF-reinforced RAC. The study further investigates the fluctuation of strain energy in FRAC under low cyclic loading, revealing the correlation between plastic strain energy and equivalent viscous damping ratio. A nonlinear viscous damping model that accounts for the influence of the reinforcing index (RI) is proposed. This model effectively predicts the degradation of strength, the evolution of plastic strain, and the dynamics of nonlinear viscous damping in composite materials with varying fiber content. Ultimately, this research provides essential technical insights for the practical engineering application of RAC.

Nonlinear hydrodynamic assessment of a floating solar double-hull substructure using viscous numerical wave tank

This paper assesses a viscous numerical solver for hydrodynamic simulations of floating double-hull substructures supporting solar panels, critical for advancing floating solar technologies. Using the OpenFOAM repository, the study develops a model based on the Finite Volume method and Volume of Fluid approach, focusing on a range of wave frequencies, from weakly to strongly nonlinear, at intermediate depths. A free decay test calibrated the mesh morphology of the control volume, enabling comparative analysis of single and double-cylinder structures exposed to Stokes second-order nonlinear waves, alongside nonlinear potential models and experimental data. Spectral analysis of these solutions quantifies the nonlinearities' influence on structural responses and high-order dynamic prediction accuracy. The key findings demonstrate that the viscous model accurately predicted heave and surge responses, outperforming the potential model under steep waves. The gap distance between the cylinder in the double-cylinder platforms significantly affects fluid flow and stability, especially under shorter waves. Accurate wave-body simulations require appropriate mesh resolution and tailored wavemaker functions for nonlinear waves. These findings highlight the need to incorporate viscous effects in floating solar platform design to enhance stability and performance in real-world environments.

Numerical and experimental investigation of the effect of interstitial liquid viscosity on the collapse of wet granular columns

The collapse of wet granular columns with high- and low-viscosity interstitial liquid is investigated through experiments and numerical simulations. By incorporating both capillary and viscous force models of interstitial liquid in the Discrete Element Method (DEM), simulations have been conducted and reproduced consistent collapse processes with the experiment. The influence of water content, contact angle, particle diameter, liquid surface tension, and viscosity is explored over a large parameter space using DEM. For wet granular columns with low-viscosity interstitial liquid of water, the final profile of the collapsed column can be predicted by Bond number (Bo), a ratio of particle gravity to capillary force. For wet granular columns where the inertial effect dominates and both capillary and viscous forces are significant, dimensional analysis is employed to characterize the collapse, indicating that the collapsed profile can be predicted by Bo and Galileo number (Ga). Using water and silicone oils with different viscosities as interstitial liquids, simulations show that the collapsed profile depends on Bo with a low capillary number (Ca ∼ 10−3), Bo and Ga when Ca is intermediate (Ca ∼ 10−1). When Ca is high (Ca > 100), the final profile is solely controlled by Bo and a rolling-collapsed regime is observed.

Finite element modeling of the glass sealing process for solid oxide cell stacks

The sealing process for solid oxide fuel cell (SOFC) and solid oxide electrolysis cell (SOEC) stacks is a vital step in the assembly and manufacturing of these systems. The cell seal and stack seal serve to prevent leakage and the mixing of air with hydrogen and steam during operation. Good seals are critical for reporting accurate cell and stack performance and durability, as leaks can mask degradations and manifest as performance improvement. Predictive modeling of seal materials during sealing processes for SOFC and SOEC stacks has been largely unexplored and could provide design and manufacturing insights for these systems. In this work, finite element modeling was conducted to simulate the assembly and stack sealing of planar cells to capture the densification, viscous flow, and crystallization behavior of the G18 glass ceramic seal material during full scale stack fabrication. The Skorohod-Olevsky viscous sintering material model was implemented in the ANSYS finite element program and modified to account for crystallization effects to simulate the response of the G18 seal material. The effects of initial cell/stack curvature were captured via preliminary stack manufacturing simulations, and its influence on stack sealing quality was studied. Effects of compressive loading sequence and configuration were investigated.

Cutoff Ergodicity Bounds in Wasserstein Distance for a Viscous Energy Shell Model with Lévy Noise

This article establishes explicit non-asymptotic ergodic bounds in the renormalized Wasserstein–Kantorovich–Rubinstein (WKR) distance for a viscous energy shell lattice model of turbulence with random energy injection. The system under consideration is driven either by a Brownian motion, a symmetric α\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\alpha $$\\end{document}-stable Lévy process, a stationary Gaussian or α\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\alpha $$\\end{document}-stable Ornstein–Uhlenbeck process, or by a general Lévy process with second moments. The obtained non-asymptotic bounds establish asymptotically abrupt thermalization. The analysis is based on the explicit representation of the solution of the system in terms of convolutions of Bessel functions.

A new approach for artificial pollination in walnut trees: AirPoll

Pollination is the first step in the plant's fruit development. Therefore, fruit setting does not occur without pollination. Some problems encountered in natural pollination cause pollination not to be achieved as desired and cause significant losses in yield and fruit quality. Artificial pollination applications with drones are the best way to solve these problems. In this study, the AirPoll artificial pollination machine, which performs artificial pollination through the air using drone technology, was developed and the operating success of the machine was tested in walnut gardens. In the experiment gardens, female flowers on 18 branches of 5 trees each in the artificially pollinated area with a drone and in the control area were marked with colored strings. Control trees were selected from a distance that would not be possible to transport pollen with a drone. As a result of the study carried out in 2020 and 2021, the average fruit setting rate in trees pollinated by drone was determined as 94.61%. In control trees, 32.33% fruit setting was achieved. Thus, it was determined that the productivity increase in artificial pollination with AirPoll was 62.28%. In addition, in the study, Computational Fluid Dynamics (CFD) simulation analysis was performed using ANSYS Fluent 2024 R1 software to predict the downward air flow and pollen distribution in the walnut tree crown. The analysis was carried out in 680 iterations using drone propellers at a rotation speed of 4500 rpm, 4 m/s airflow and a k-w viscous model. In the analysis, it was observed that the pollen was distributed homogeneously with the determined height and the created artificial pollination environment. Based on the results obtained from the simulations, a convergence criterion of 5e−3 for continuity and 1e−6 for speed, k, w was determined. Considering all the results, the ease of use of the developed AirPoll artificial pollination machine and the successful results obtained in field trials reveal the effectiveness of the AirPoll artificial pollination machine.

Sensitivity analysis of a dense discrete phase model for 3D simulations of a tapered fluidized bed

This study aims to conduct a sensitivity analysis of closure models and modeling parameters for the Dense Discrete Phase Modeling (DDPM) approach in order to investigate the hydrodynamics of a 3D lab-scale Tapered Fluidized Bed (TFB). The closure models and model parameters under investigation include the gas-solid drag force, viscous models, particle-particle interaction models, restitution coefficient, specularity coefficient, and rebound coefficient. The primary objective of this sensitivity analysis is to optimize the numerical model's performance. The numerical results, in terms of axial and lateral Solid Volume Fraction (SVF) profiles obtained from the sensitivity analysis, indicate that the drag force and restitution coefficient significantly influence the hydrodynamics of the TFB. Properly selecting these parameters could result in the improved performance of the numerical model. However, the sensitivity of turbulence models, particle-particle interaction models, specularity coefficient, and rebound coefficient has a lesser impact on the hydrodynamics results. This work concludes with the recommendation of a set of closure models and modeling parameters that offer the most accurate prediction of the hydrodynamics of the TFB.

An Expanding Accretion Disk and a Warm Disk Wind as Seen in the Spectral Evolution of HBC 722

We present a comprehensive analysis of the post-outburst evolution of the FU Ori object HBC 722 in optical/near-infrared (NIR) photometry and spectroscopy. Using a modified viscous accretion disk model, we fit the outburst epoch spectral energy distribution to determine the physical parameters of the disk, including Ṁacc=10−4.0M⊙ yr−1, R inner = 3.65 R ⊙, i = 79°, and a maximum disk temperature of Tmax=5700 K. We then use a decade of optical/NIR spectra to demonstrate a changing accretion rate drives the visible-range photometric variation, while the NIR shows the outer radius of the active accretion disk expands outward as the outburst progresses. We also identify the major components of the disk system: a plane-parallel disk atmosphere in Keplerian rotation and a two-part warm disk wind that is collimated near the star and wide-angle at larger radii. The wind is traced by classic wind lines, and appears as a narrow, low-velocity, deep absorption component in several atomic lines spanning the visible spectrum and in the CO 2.29 μm band. We compare the wind lines to those computed from wind models for other FU Ori systems and rapidly accreting young stellar disks and find a 4000–6000 K wind can explain the observed line profiles. Fitting the progenitor spectrum, we find M * = 0.2 M ⊙ and Ṁprogenitor=7.8×10−8M⊙yr−1 . Finally, we discuss HBC 722 relative to V960 Mon, another FU Ori object we have previously studied in detail.

Periodic response and stability analysis of a bistable viscoelastic von Mises truss

This paper examines the effect of viscoelasticity on the periodic response of a lumped parameter viscoelastic von Mises truss. The viscoelastic system is described by a second-order equation that governs the mechanical motion coupled to a first-order equation that governs the time evolution of the viscoelastic forces. The viscoelastic force evolves at a much slower rate than the elastic oscillations in the system. This adds additional time scales and degrees of freedom to the system compared to its viscous counterparts. The focus of this study is on the system’s behavior under harmonic loading, which is expected to show both regular and chaotic dynamics for certain combinations of forcing frequency and amplitude. While the presence of chaos in this system has already been demonstrated, we shall concentrate only on the periodic solutions. The presence of the intrawell and interwell periodic oscillations is revealed using the Harmonic Balance method. The study also looks at the influence of parameter changes on the system’s behavior through bifurcation diagrams, which enable us to identify optimal system parameters for maximum energy dissipation. Lastly, we formulate an equivalent viscous system using an energy-based approach. We observe that a naive viscous model fails to capture the behavior accurately depending on the system and excitation parameters, as well as the type of excitation. This underscores the necessity to study the full-scale viscoelastic system.

Recursive and batch Bayesian estimation of exponential non-viscous damping systems

Non-viscous damping systems include a convolutional integral and a kernel function in their equation of motion to incorporate time-hysteresis damping effects, which are present in dynamical behavior of most engineering materials yet are absent in commonly used viscous damping models. When an exponential kernel function is adopted by the non-viscous model, the unique damping characteristic is realized by an additional model parameter known as the relaxation parameter. The objective of this paper is to investigate various aspects of estimation problems on exponential non-viscous damping systems through recursive and batch Bayesian time-domain frameworks, with a focus on how the relaxation parameter introduces additional complexity in estimation problems compared to viscous damping systems. Two well-established algorithms are employed: the unscented Kalman filter (UKF) for recursive Bayesian estimation and the transitional Markov Chain Monte Carlo (TMCMC) for batch Bayesian estimation. We first analyze the complexity of estimation problems in SDOF viscous and non-viscous damping systems. The TMCMC algorithm offers a quantitative analysis that reveals greater uncertainty and stronger parameter correlation in non-viscous damping systems compared to viscous damping systems. Subsequently, the same SDOF systems are utilized to study recursive Bayesian estimation via UKF such as the effects of measurement data type, discretization, and initial conditions. Based on the results of the TMCMC algorithm, we study the dependence of UKF performance on the initial condition for various SDOF non-viscous damping systems with different levels of non-viscosity. In the end, a laboratory experiment compares the estimation results between viscous and non-viscous damping systems using both TMCMC and UKF.

Reconsidering bulk viscosity in Brans–Dicke theory

In this paper, we reconsider the concept of bulk viscosity in Brans–Dicke theory to study accelerated expansion of the universe in a flat Friedmann–Robertson–Walker metric. In recent works on bulk viscosity in Brans–Dicke theory, the power-law form of Brans–Dicke scalar field has been taken to explain recent phase transition of the universe, however, power-law form confronts constant deceleration parameter problem. Therefore, we consider recently proposed well-motivated logarithmic form of Brans–Dicke scalar field to discuss bulk viscous model in Brans–Dicke theory. We obtain the values of deceleration parameter and equation of state parameter for the model, and plot their graphs against the redshift parameter z. The plots show that the model is able to explain the recent phase transition of the universe and equation of state parameter shows the behavior of dark energy. Further, we apply two important analysis, namely, [Formula: see text] analysis and thermodynamic analysis to examine our model. The [Formula: see text] analysis shows that our model belong to thawing region and shows similarities with quintessence model. All the trajectories start from the point [Formula: see text] with different negative values of w having quintessence behavior. The thermodynamic analysis shows that the model satisfies generalized second law of thermodynamics.

Asymptotic stability of rarefaction wave and boundary layer for outflow problem on the viscous vasculogenesis model *

In this paper, we are concerned with the outflow problem on a simplified viscous vasculogenesis model in the half-line R+ . Firstly, we establish the global-in-time asymptotic stability of the rarefaction wave. Secondly, we obtain the unique existence and decay property of the boundary layer by using stable manifold theorem. Moreover, the asymptotic stability and convergence rates of solution towards boundary layer are obtained. The appearance of concentration makes the stationary problem more difficult than Navier–Stokes equations or Navier–Stokes–Poisson equations.

Nonuniqueness of Weak Solutions to the Dissipative Aw–Rascle Model

We prove nonuniqueness of weak solutions to multi-dimensional generalisation of the Aw-Rascle model of vehicular traffic. Our generalisation includes the velocity offset in a form of gradient of density function, which results in a dissipation effect, similar to viscous dissipation in the compressible viscous fluid models. We show that despite this dissipation, the extension of the method of convex integration can be applied to generate infinitely many weak solutions connecting arbitrary initial and final states. We also show that for certain choice of data, ill posedness holds in the class of admissible weak solutions.

Integrating the complex rheological Carreau model with the Graetz-Brinkman problem in a horizontal passage

ABSTRACT The current investigation emphasizes the influence of viscous dissipation in laminar forced convection internal flow for horizontal conduit using the non-Newtonian fluid. A Carreau fluid model is taken into account. The hydrodynamically developed velocity profile is obtained by employing a perturbation approach. A classical Graetz approach is utilized to achieve the solution of the developed energy equation while the MATLAB built-in command bvp4c is taken into account for the solution of the Eigenvalue problem. The negligible axial conduction and uniform physical characteristics are presumed. The influence of the viscous dissipation and model parameters on non-dimensional bulk temperature and Nusselt number is deliberated for both cooling and heating situations. The current analysis is valid for small values of Weissenberg number We ≤ 1 . The findings reveal that viscous dissipation has a significant impact on temperature distribution in both developing and fully established regions.

Formal derivation and existence of global weak solutions of an energetically consistent viscous sedimentation model

The purpose of this paper is to derive a viscous sedimentation model from the Navier-Stokes system for incompressible flows with a free moving boundary. The derivation is based on the different properties of the fluids; thus, we perform a multiscale analysis in space and time, and a different asymptotic analysis to derive a system coupling two different models: the sediment transport equation for the lower layer and the shallow water model for the upper one. We finally prove the existence of global weak solutions in time for model containing some additional terms.

Nature of instability in flow-driven porous anodic oxide.

Self-organized porous anodic oxide films are formed by the electrochemical oxidation of reactive metal aluminum in acidic solutions in which the oxide is soluble. Recently, viscous flow models have shown using linear stability analysis that the instability results from a trade-off between the destabilizing effect of viscous flow of oxide and the stabilizing effect of oxide formation, which provides the wavelength selection mechanism for pattern formation. Anion adsorption on surface growth sites causes nonuniform compressive stress at the oxide-solution interface, which drives the flow. This anodic instability is analogous to the classical Marangoni instability induced by surface tension gradients. In this work, nature of the instability beyond the stability threshold is determined using a weakly nonlinear analysis. For the growth of well-developed pores beyond the threshold, a subcritical nature of the instability is essential. However, our weakly nonlinear analysis shows that the solutions emerging from neutral stability are supercritical in nature at all wavenumbers for the practical range of anodizing control parameters investigated. We also determine the region where the model is Hadamard stable, a necessary condition for well-posedness.

CAI formation in the early Solar System

Calcium-aluminium-rich inclusions (CAIs) are the oldest dated solid materials in the Solar System, and are found as light-coloured crystalline ingredients in carbonaceous chondrite meteorites. Their formation time is commonly associated with age zero of the Solar System. Nevertheless, the physical and chemical processes that once led to the formation of these submillimetre- to centimetre-sized mineral particles in the early solar nebula are still a matter of debate. In this paper, we propose a pathway to form such inclusions during the earliest phases of disc evolution. We combine 1D viscous disc evolutionary models with 2D radiative transfer, equilibrium condensation, and new dust opacity calculations. We show that the viscous heating associated with the high accretion rates in the earliest evolutionary phases causes the midplane inside of about 0.5 au to heat up to limiting temperatures of about 1500–1700 K, but no further. These high temperatures force all refractory material components of the inherited interstellar dust grains to sublimate – except for a few Al-Ca-Ti oxides, such as Al2O3, Ca2Al2SiO7, and CaTiO3. This is a recurring and very stable result in all our simulations, because these minerals form a natural thermostat. Once the Mg-Fe silicates are gone, the dust becomes more transparent and the heat is more efficiently transported to the disc surface, which prevents further warming. This thermostat mechanism keeps these minerals above their annealing temperature for hundreds of thousands of years, allowing them to form large pure crystalline particles. These particles are dragged out by the viscously spreading disc, and once they reach a distance of about 0.5 au, the silicates recondense on the surface of the Ca-Al-rich particles, adding an amorphous silicate matrix. We estimate that this mechanism of CAI production works during the first 50 000 yr of disc evolution. These particles then continue to move outward and populate the entire disc up to radii of about 50 au, before the accretion rate eventually subsides, the disc cools, and the particles start to drift inwards.

Numerical Seakeeping Analysis for a Floating Helicopter After Ditching in Water

Abstract This paper investigates the seakeeping behavior of helicopters after an emergency landing in water, focusing on a Northern North Sea wave climate and considering a realistic helicopter geometry. Computational fluid dynamics techniques, including the cell-centered finite volume method and boundary element methods, were utilized to analyze motion responses and load distribution. The study ensures numerical result reliability through recommended simulation practices. Results indicate that the inviscid model produces similar outcomes to the viscous model in decay tests with roll, pitch, and heave motions. Natural periods for roll, pitch, and heave motions were obtained. Linearity between incident wave amplitude and pitch/heave response was noted for regular waves, while roll linearity was limited for small angles. In irregular wave conditions, helicopters tended to align perpendicular to waves over time, resulting in increased peak roll angles with higher significant wave heights. Exceedance rates of maximum roll peaks, useful for the assessment of capsizing probability, were quantified for different significant wave heights.

Differential proliferation regulates multi-tissue morphogenesis during embryonic axial extension: integrating viscous modeling and experimental approaches.

A major challenge in biology is to understand how mechanical interactions and cellular behavior affect the shapes of tissues and embryo morphology. The extension of the neural tube and paraxial mesoderm, which form the spinal cord and musculoskeletal system, respectively, results in the elongated shape of the vertebrate embryonic body. Despite our understanding of how each of these tissues elongates independently of the others, the morphogenetic consequences of their simultaneous growth and mechanical interactions are still unclear. Our study investigates how differential growth, tissue biophysical properties and mechanical interactions affect embryonic morphogenesis during axial extension using a 2D multi-tissue continuum-based mathematical model. Our model captures the dynamics observed in vivo by time-lapse imaging of bird embryos, and reveals the underestimated influence of differential tissue proliferation rates. We confirmed this prediction in quail embryos by showing that decreasing the rate of cell proliferation in the paraxial mesoderm affects long-term tissue dynamics, and shaping of both the paraxial mesoderm and the neighboring neural tube. Overall, our work provides a new theoretical platform upon which to consider the long-term consequences of tissue differential growth and mechanical interactions on morphogenesis.