Dumbbell Model Research Articles

Global existence of 2-D FENE Dumbbell Model with concentrated center-of-mass

In this paper, we prove global existence of smooth solutions to the two dimensional FENE (Finite Extensible Nonlinear Elastic) systems with an extra concentrated center-of-mass diffusion.

Optimal decay rates of weak solutions for the 2D co-rotation FENE dumbbell model of polymeric flows

There is a long standing problem conjectured by Schonbek (2009), whether the sharp decay of velocity field for the 2D co-rotation FENE dumbbell model of polymeric flows should be (1+t)−12. By using the generalized Fourier splitting methods, we improve the result of Luo and Yi (2019) and solve Schonbek’s conjecture completely.

A Novel 3D Model for Visualization and Tracking of Fibroblast-Guided Directional Cancer Cell Migration.

Simple SummaryRecent advances in 3D cell culture have provided new opportunities for investigating interactions between cancer cells and their surrounding stromal cells. The 3D culture platform described herein is both time efficient and economical in the study of direct cell–cell interactions. The unique design of our dumbbell model had allowed us to visualize and monitor the entire recruitment process of cancer cells by fibroblasts under an in vitro condition. Suitable for almost every cell type, our model has the potential for a wider application as it can be adapted for use in drug screening and the study of cellular factors involved in cell–cell attraction.Stromal fibroblasts surrounding cancer cells are a major and important constituent of the tumor microenvironment not least because they contain cancer-associated fibroblasts, a unique fibroblastic cell type that promotes tumorigenicity through extracellular matrix remodeling and secretion of soluble factors that stimulate cell differentiation and invasion. Despite much progress made in understanding the molecular mechanisms that underpin fibroblast–tumor cross-talk, relatively little is known about the way the two cell types interact from a physical contact perspective. In this study, we report a novel three-dimensional dumbbell model that would allow the physical interaction between the fibroblasts and cancer cells to be visualized and monitored by microscopy. To achieve the effect, the fibroblasts and cancer cells in 50% Matrigel suspension were seeded as independent droplets in separation from each other. To allow for cell migration and interaction, a narrow passage of Matrigel causeway was constructed in between the droplets, effectively molding the gel into the shape of a dumbbell. Under time-lapse microscopy, we were able to visualize and image the entire process of fibroblast-guided cancer cell migration event, from initial vessel-like structure formation by the fibroblasts to their subsequent invasion across the causeway, attracting and trapping the cancer cells in the process. Upon prolonged culture, the entire population of fibroblasts eventually infiltrated across the passage and condensed into a spheroid-like cell mass, encapsulating the bulk of the cancer cell population within. Suitable for almost every cell type, our model has the potential for a wider application as it can be adapted for use in drug screening and the study of cellular factors involved in cell–cell attraction.

Coupled attitude-vibration analysis of an E-sail using absolute nodal coordinate formulation

In this study, the effects of solar wind on an electric sail (E-sail) are modeled and analyzed using an absolute nodal coordinate formulation (ANCF). First, the thrust of the charged metal tether that makes up the E-sail was analyzed and a model was established. Numerical simulations of a single metal tether were performed. Then, an overall E-sail model was established using the connection matrix, and E-sails subjected to different angular velocities were compared. Simulation results of the ANCF model and a dumbbell model were compared at different angular velocities. The results confirm that with a relatively high angular velocity, the flexible metal chain can be approximately regarded as a rigid body. However, with a small angular velocity, the flexibility of the metal chain cannot be ignored.

Domestication past and future of tribal agriculture in Bastar

Wild edible fruits play an important role in the nutrition, medicinal and traditional lifestyles of the local people. Bastar region is rich in its biodiversity and tribal communities who are dependent on wild resources for the sustenance. The main forest is sal, Harra, Bahera, Char, Tendu, Palash. Most of the people are either engaged in livelihood through agriculture or forestry-related options. The economic condition of the people is also below the national level as reflected in per capita income. Wild edible fruits of this region are not only consumed but are also sold in local markets. There is a need to domesticate the fruits at the same time there is a need to develop cultivable improved varieties and the study nutritional aspect to design better foods for the future. Although these wild edible plants play an important role in food security, they are ignored. The primitive man through trial and error has selected many wild edible plants, which are edible and subsequently domesticated them. Allopatric speciation, also referred to as geographic speciation, vicariant speciation, or its earlier name, the dumbbell model, is a mode of speciation that occurs when biological populations of the same species become isolated from each other to an extent that prevents or interferes with gene flow. Wild edible is less susceptible to diseases, can be grown easily without the application of pesticides. Ironically these plants are still unknown or less known to other parts of the world. The wild edible plant species will be popularized after phytochemical analysis and nutritional studies. The present study on the review of “Domesticable Hidden Wild Botanical Gems of Forest” will be helpful in pooling different types of edible plant species utilized by various tribes in different parts of the forest.

Direct Numerical Simulations of Turbulent Channel Flow With Polymer Additives

ABSTRACTDirect numerical simulations have been applied to simulate flows with polymer additives. FENE-P (finite-extensible-nonlinear-elastic-Peterlin) dumbbell model solving for the conformation tensor is adopted to investigate the influence of the polymer on the flowfield. Boundary treatments of the conformation tensor on the flowfield are examined first, where boundary condition based on the linear extrapolation scheme provides more accurate results with second-order accurate error norms. Further simulations of the turbulent channel flow at different Weissenberg numbers are also conducted to investigate the influence on drag reduction. Drag reduction increases in tandem with the increase of Weissenberg number and the increase saturates at Weτ~200, where the drag reduction is close to the maximum drag reduction (MDR) limit. At the regime of y+ > 5, the viscous layer thickens with the increase of the Weissenberg number showing a departure from the traditional log-law profile, and the velocity profiles approach the MDR line at high Weissenberg number. The Reynolds stress decreases in tandem with the increase of Weτ, whereas the levels of laminar stress and polymer stress act adversely. However, as the Weissenberg number increases, the proportion of the laminar stress in the total stress increases, and this contributes to the drag reduction of the polymer flow.

Analysis of Stabilized Crank-Nicolson Time-Stepping Scheme for the Evolutionary Peterlin Viscoelastic Model

The Peterlin viscoelastic model describes the motion of certain incompressible polymeric fluids. It employs a nonlinear dumbbell model with a nonlinear spring force law making it more nonlinear than other viscoelastic models. In this paper, we propose and study a fully implicit stabilized Crank-Nicolson time stepping scheme for finite element spatial discretization of the non-stationary Peterlin viscoelastic fluid model with non-homogeneous boundary conditions. The proposed scheme adds a suitable stabilizing term to improve the structural and stability properties of the scheme. We prove that the scheme is almost unconditionally stable, i.e., stable when the time step is less than or equal to a constant. Further, with the help of the a priori error bounds of the Stokes and Ritz projections, optimal error estimates for the velocity, the conformation tensor and the pressure are presented in suitable norms. Numerical examples are presented that illustrate the accuracy and stability of the scheme.

The effect of latitude and PM2.5 on spreading of SARS-CoV-2 in tropical and temperate zone countries

The present work describes spreading of Severe Acute Respiratory Syndrome Coronavirus-2 (SARS-CoV-2) at the tropical and temperate zones which are explained based on insolation energy, Particulate Matter (PM2.5), latitude, temperature, humidity, Population Density (PD), Human Development Index (HDI) and Global Health Security Index (GHSI) parameters. In order to analyze the spreading of SARS-CoV-2 by statistical data based on the confirmed positive cases which are collected between December 31, 2019 to April 25, 2020. The present analysis reveals that the outbreak of SARS-CoV-2 in the major countries lie on the Equator is 78,509 cases, the countries lie on the Tropic of Cancer is 62,930 cases (excluding China) and the countries lie on the Tropic of Capricorn is 22,842 cases. The tropical countries, which comes between the Tropic of Cancer and Tropic of Capricorn is reported to be 1,77,877 cases. The temperate zone countries, which are above and below the tropical countries are reported to be 25,66,171 cases so, the pandemic analysis describes the correlation between latitude, temperate zones, PM2.5 and local environmental factors. Hence, the temperature plays a pivotal role in the spreading of coronavirus at below 20 °C. The spreading of SARS-CoV-2 cases in Northern and Southern Hemispheres has inverse order against absorption of insolated energy. In temperate zone countries, the concentration of PM2.5 at below 20 μg/m3 has higher spreading rate of SARS-CoV-2 cases. The effect of insolation energy and PM2.5, it is confirmed that the spreading of SARS-CoV-2 is explained by dumb-bell model and solid/liquid interface formation mechanism. The present meta-analysis also focuses on the impact of GHSI, HDI, PD and PM2.5 on spreading of SARS-CoV-2 cases.

Chaos in a tethered satellite system induced by atmospheric drag and Earth’s oblateness

This paper describes the chaos behavior of an in-plane tethered satellite system induced by atmospheric drag and the Earth’s oblateness. A commonly used model, the dumbbell model, for tethered satellite systems is employed in this study. After taking the atmospheric drag and the Earth’s oblateness into account, the complicated dynamics of chaotic features are observed in the pitch motion of the dumbbell model. Afterward, the existence of the chaos is computed by transversal heteroclinic orbits, and accordingly, the parameter domain for the occurrence of chaos is obtained by the Melnikov function. Furthermore, a tether length control based on a sliding-mode controller is proposed to suppress the chaotic motion. Finally, the numerical simulations in this paper demonstrate the occurrence of the chaotic phenomenon and its control performance.

Accuracies of 3D printers with hard and soft materials

PurposeThis study aims to systemically evaluate morphological printing errors between computer-aided design (CAD) and reference models fabricated using two different three-dimensional printing (3DP) technologies with hard and soft materials.Design/methodology/approachThe reference models were designed to ensure simpler and more accurate measurements than those obtained from actual kidney simulators. Three reference models, i.e. cube, dumbbell and simplified kidney, were manufactured using photopolymer jetting (PolyJet) with soft and hard materials and multi-jet printing (MJP) with hard materials. Each reference model was repeatably measured five times using digital calipers for each length. These values were compared with those obtained using CAD.FindingsThe results demonstrate that the cube models with the hard material of MJP and hard and soft materials of PolyJet were smaller (p = 0.022, 0.015 and 0.057, respectively). The dumbbell model with the hard material of MJP was smaller (p = 0.029) and that with the soft material of PolyJet was larger (p = 0.020). However, the dumbbell with the hard material of PolyJet generated low errors (p = 0.065). Finally, the simplified kidney models with the hard material of MJP and soft materials of PolyJet were smaller (p = 0.093 and 0.021) and that with the hard material of PolyJet was opposite to the former models (p = 0.043).Originality/valueThis study, to the best of authors’ knowledge, is the first to determine the accuracy between CAD and reference models fabricated using two different 3DP technologies with multi-materials. Thus, it serves references for surgical applications as simulators and guides that require accuracy.

A charged finitely extensible dumbbell model: Explaining rheology of dilute polyelectrolyte solutions

A robust non-Newtonian fluid model of dilute polyelectrolyte solutions is derived from kinetic theory arguments. Polyelectrolyte molecules are modeled as finitely elongated nonlinear elastic dumbbells, where effective charges (interacting through a simple Coulomb force) are added to the beads in order to model the repulsion between the charged sections of polyelectrolyte chains. It is shown that the relative strength of this repulsion is regulated by the electric-to-elastic energy ratio, E, which is one of the key parameters of the model. In particular, E accounts for the intrinsic rigidity of polyelectrolyte molecules and can be used to explain the impact of solvent salinity on polyelectrolyte rheology. With two preaveraging approximations, the constitutive equations of the resulting fluid model are formulated in closed form. Material functions predicted by the model for steady shear flow, steady extensional flow, small-amplitude oscillatory shear flow, and start-up and cessation of steady shear flow are obtained and investigated using a combination of analytical and numerical methods. In particular, it is shown how these material functions depend on E. The two limiting cases of the model—uncharged dumbbells (E = 0) and rigid dumbbells (E → ∞)—are included in the analysis. It is found that despite its simplicity, the model predicts most of the experimentally observed rheological features of polyelectrolyte solutions.

Asymmetric flows of complex fluids past confined cylinders: A comprehensive numerical study with experimental validation

Three non-Newtonian constitutive models are employed to investigate how fluid rheological properties influence the development of laterally asymmetric flows past confined cylinders. First, simulations with the shear-thinning but inelastic Carreau–Yasuda model are compared against complementary flow velocimetry experiments on a semidilute xanthan gum solution, showing that shear-thinning alone is insufficient to cause flow asymmetry. Next, simulations with an elastic but non-shear-thinning finitely extensible non-linear elastic dumbbell model are compared with experiments on a constant viscosity solution of poly(ethylene oxide) (PEO) in an aqueous glycerol mixture. The simulations and the experiments reveal the development of an extended downstream wake due to elastic stresses generated at the stagnation point but show no significant lateral asymmetries of the flow around the sides of the cylinder. Finally, the elastic and shear-thinning linear Phan–Thien–Tanner (l-PTT) model is compared with experimental velocimetry on a rheologically similar solution of PEO in water. Here, at low flow rates, lateral symmetry is retained, while the growth of a downstream elastic wake is observed, in qualitative similarity to the non-shear-thinning elastic fluids. However, above a critical flow rate, the flow bifurcates to one of the two stable and steady laterally asymmetric states. Further parameter studies with the l-PTT model are performed by varying the degrees of shear-thinning and elasticity and also modifying the confinement of the cylinder. These tests confirm the importance of the coupling between shear-thinning and elasticity for the onset of asymmetric flows and also establish stability and bifurcation diagrams delineating the stable and unstable flow states.

Dissipation in Langevin Equation and Construction of Mobility Tensor from Dissipative Heat Flow

The rheological behavior of a material is strongly related to the energy dissipation, and the understanding and modeling of dissipation is important from the view point of rheology. To study rheological properties with some mesoscopic and macroscopic dynamics models, the modeling of dynamic equation which appropriately incorporates the dissipation is important. Although there are several methods to construct mesoscopic and macroscopic dynamic equations, such as the Onsager's method, their validity is not fully clear. In this work, we theoretically analyze the dissipation in a mesoscopic Langevin equation in detail, from the view point of stochastic energetics. We show that the dissipative heat flow from the heat bath to the system plays an important role in the mesoscopic dynamics. The dissipative heat flow is unchanged under the variable transform, and thus it is a covariant quantity. We show that we can construct the Langevin equation and also perform a coarse-graining based on the dissipative heat flow. We can derive the mobility tensor from the dissipative heat flow, and construct the Langevin equation by combining it and the free energy. Our method can be applied to various systems, such as the dumbbell model and the diffusion type equation for the density field, to give the coarse-grained dynamic equations for them.

In situ dielectric characterization of dynamic orientation for polymer molecular chains

Polymer orientation is a fundamental and key issue, exhibiting crucial impacts on physical properties of polymeric parts. Current methods are limited in transparent materials and fail to measure the dynamic orientation in industrial polymer processing in situ. Herein, we reported an innovative strategy that dynamic orientation for polymer molecular chains was successfully characterized in situ by dielectric method. A key dielectric-orientation theoretical model was established, and a facile interdigital electrode capacitor (IDEC) array sensor was designed. The experimental results not only agreed well with the classic elastic dumbbell model and the traditional optical measurement method, but also showed a universal applicability for different polymer solutions and a good application prospect in injection molding process. Investigated results showed that the orientation difference of 1 wt% PVDF/DMF, 1 wt% PVC/DMF and 1 wt% PS/DMF solution was 0.57, 0.97 and 0.75 at shear rate 0–407 1/s, respectively. Additionally, the method was successfully applied in injection molding (Δε, 0.25–0.88 under shear rate 56.6–250 1/s). Our strategy built a new ‘decoding fingerprint’ to the dynamic orientation of polymer.

Adaptive sliding mode control for deployment of electro-dynamic tether via limited tension and current

This paper studies the deployment control of the electrodynamic tether system by means of tether tension and electric current regulation. Design of the control strategy has been implemented based on the simplified dumbbell model. In order to improve the robustness of the control system to the possible external disturbances, an adaptive sliding mode control is proposed to deploy the tether to the local vertical with the consideration of input limitations, which are introduced by a pair of saturation functions to ensure that the tether tension is always non-negative and the current is within limits. In addition, the proposed adaptive law is intended to estimate the mass parameter of the model, which is with uncertainty caused by the difficulty in accurately determining the masses of the end-bodies. The stability characteristic of the system under the proposed hybrid controller is studied based on the Lyapunov theory. Numerical case studies in the different orbital inclinations are conducted to illustrate the effectiveness of the proposed control strategy. Moreover, the performance of the controller is presented in the presence of the initial perturbations, the external disturbances and the uncertainty of mass parameter of the system.

Pressure in rigid body molecular dynamics

We present a detailed derivation of the expression for the pressure in MD simulations that contain rigid bodies, where two equivalent formulations have been developed. One of these formulations was used in HOOMD-blue v1.x, but implemented incorrectly. We point out the precise reason for this implementation issue, the difference with the current and correct implementation in HOOMD-blue v2.x, and lessons learned. We perform numerical validation tests using dumbbell models, a mixture of cubic and spherical particles, and the SPC/E water model.

Dumbbell kinetic theory for polymers in a combination of flow and external electric field.

Combining Poiseuille flow with an external electric field is a demonstrated method to drive transverse migration in capillary electrophoresis. Despite both computational and experimental studies, a number of questions about how to best model polymers under these conditions remains. Attempts have been made to develop a kinetic theory for a bead-spring dumbbell model, but these have only been accurate at low electric field strength and have not captured the nonmonotonic relationship between migration and electric field strength. In this paper, we revisit the development of a kinetic theory for a bead-spring dumbbell in a combination of parabolic flow and an external electric field. The resultant theory yields a compact formula that predicts polymer concentration profiles that agree excellently with our Brownian dynamics simulations including the aforementioned nonmonotonic relationship. Furthermore, we compare our theoretical results to experimental data and find that our model nearly quantitatively predicts the position of the maximum in migration.

Simulation of the absolute permeability based on the capillary pressure curves using the dumbbell model

The paper deals with simulation of absolute permeability of granular collectors based on the capillary pressure curves using the dumbbell model. It has been established that for assessing permeability based on the capillary data, effective porosity should be used, since residual water does not participate in the displacement of fluid from the rock sample. It was proved that when using the dumbbell model instead of a simple capillary model, accuracy of absolute permeability prediction based on the capillary pressure curves increases significantly.

Effect of Inertia on Linear Viscoelasticity of Harmonic Dumbbell Model

The overdamped (inertialess) dumbbell model is widely utilized to study rheological properties of polymers or other soft matters. In most cases, the effect of inertia is merely neglected because the momentum relaxation is much faster than the bond relaxation. We theoretically analyze the effect of inertia on the linear viscoelasticity of the harmonic dumbbell model. We show that the momentum and bond relaxation modes are kinetically coupled and the inertia can affect the bond relaxation if the momentum relaxation is not sufficiently fast. We derive an overdamped Langevin equation for the dumbbell model, which incorporates the weak inertia effect. Our model predicts the bond relaxation dynamics with the weak inertia effect correctly. We discuss how the weak inertia affects the linear viscoelasticity of a simple harmonic dumbbell model and the Rouse model.

Viscous drag and rod orientation kinematics in an orthotropic fluid

A model is proposed, where the evolution of the orientation of each fiber is coupled to the orientations of the surrounding fibers in the flow of a fiber-filled fluid and includes the effects of the fiber volume fraction and aspect ratio. This is performed by accounting for the effective behavior of the fiber-filled fluid, which is anisotropic although the fibers are embedded in an isotropic Newtonian fluid. The rotation of a fiber in these conditions is predicted by a dumbbell model, which allows an extension of Jeffery’s equation to anisotropic cases. This involves the numerical evaluation of the drag force applied on a sphere in an orthotropic incompressible fluid, which is evaluated by finite element simulations. A simple fit is proposed for the practical use of the coupled model, which is applied finally to the orientation kinematics of a population of fibers in a simple shear flow, and the results are compared with the ones given by the standard uncoupled approach.