Present 2D Model Research Articles

Dynamics of Thermocapillary-Driven Motion of Liquid Drops.

The thermocapillary migration of a drop placed on a solid plate is examined. The Brochard model using the lubrication approximation provides both Marangoni and Poiseuille flow components. The present 2D model extends Brochard analysis and provides a solution for the dynamics of drop migration using extended boundary conditions at the advancing and receding contact lines to account for both Marangoni and Poiseuille flow components, derived approximate drop profiles, and conservation of mass. The model is analytical, and the results are presented in a dimensionless form. The effects of the temperature gradient, surface tension coefficient to surface tension ratio, liquid viscosity, and static advancing and receding contact angles on migration dynamics are analyzed.

Two-dimensional elasticity model for composite beams with deformable shear connectors: Analytical and numerical solutions

A novel and efficient exact two-dimensional (2D) model is developed for predicting the flexural response of two-layered composite beams made of different materials based on the elasticity theory. The beam is considered as a specific case of plane stress problem laying in the longitudinal vertical plane passing through the centroid of the beam section. The proposed two-dimensional model considers the orthotropic properties of materials used in composite beams. The partial shear interaction between two material layers in the form of shear slip at their interface is also considered in this study. The deformable shear connectors between these layers are modeled using distributed shear springs along the beam length. The present 2D model's accuracy is validated by comparing its results with published results as well as numerical results generated by a thorough 2D finite element model using ABAQUS. Furthermore, the stretching effect over the direction of beam depth on the flexural response of two-layered composite beams is investigated by comparing the results produced by the one-dimensional (1D) HBT model and the proposed 2D elasticity model.

Skyrmion crystal in the RKKY system on the two-dimensional triangular lattice

We study the ordering properties of the isotropic RKKY Heisenberg model on the two-dimensional (2D) triangular lattice by extensive Monte Carlo simulations to get insights into the chiral-degenerate skyrmion crystal (SkX) of metallic magnets. Our Hamiltonian contains only the spin-quadratic RKKY interaction derived from the spherical Fermi surface, containing neither the nesting nor the many-body interaction. The SkX phase is stabilized under applied fields where the frustration associated with the oscillating nature of the RKKY interaction and the emergent many-body interactions generated by thermal fluctuations play important roles. Replica symmetry breaking, reported in our recent study on the 3D RKKY model [Phys. Rev. B 104, 184432 (2021)], turns out to be absent in the present 2D model. Implications to the SkX formation mechanism are discussed.

Semi-empirical estimation of the Zagreb ML 5.5 earthquake (2020) ground motion amplification by 1D equivalent linear site response analysis

The 22 March 2020 Zagreb ML 5.5 earthquake ground shaking resulted in damage to buildings and infrastructure. The most affected buildings were older and cultural heritage buildings (built before 1963) in the old city centre with significant damage extent in the epicentral zone (southeastern foothills of Medvednica Mt.). This study presents site response analysis on the realistic site profiles from the epicentre towards the accelerometric stations QUHS and QARH and comparison with strong motion data recorded during the Zagreb 2020 earthquake. Semi-empirical estimation of the ground motion amplification (i.e., peak ground acceleration at surface) showed that modelled and recorded values are comparable. Moreover, we present 2D model of peak ground acceleration at surface (PGAsurf ) variation for the superimposed site profile from the epicentre towards two accelerometric stations. Ground motion amplification for the Zagreb ML 5.5 earthquake scenario showed that PGAsurf is larger by a factor of 2 than the bedrock value (approx. 0.35 g in the epicentre and 0.20 g on the 12 km distant accelerometric station). This study is a contribution to better understanding of the Zagreb ML 5.5 earthquake effects and significance of local site effects in the damage extent, something that combined with older and heritage buildings resulted in high economic consequences. Therefore, it is important that site-specific ground motion simulation and seismic microzonation of the Zagreb continues with installation of an accelerometric array. This is very important for earthquake retrofitting and resilience of the low, mid- and high-rise buildings with particular care of cultural and historical buildings as well for the further urban planning.

Interacting adipose-derived stem cells and microvascular endothelial cells provide a beneficial milieu for soft tissue healing.

There is growing evidence suggesting that healing of chronic soft tissue wounds profits from the presence of adipose-derived stem cells (ADSC). Among the large spectrum of mechanisms by which ADSC might act, especially the interaction with the microvascular endothelial cell, a main player during angiogenesis, is of special interest. In the present 2D model on the basis of endothelial cell ADSC co-cultures, we focused on the identification of characteristics of both cell types in response to a typical condition in acute and chronic wounds: hypoxia. Parameters like proliferation capacity, migration, myofibroblastoid differentiation of ADSC and the quantification of important paracrine factors related to angiogenesis and inflammation were used to correlate our experimental model with the in vivo situation of soft tissue healing. ADSC were not negatively affected by hypoxia in terms of proliferation, referring to their excellent hypoxia tolerance. Myofibroblastoid differentiation among ADSC was enhanced by hypoxia in mono- but not in co-culture. Furthermore, co-cultures were able to migrate under hypoxia. These effects might be caused to some extent by the distinct milieu created by interacting ADSC and endothelial cells, which was characterized by modulated levels of interleukin-6, interleukin-8, monocyte chemoattractant protein-1 and vascular endothelial growth factor. The identification of these cell characteristics in the present 2D in vitro model provide new insights into the process of human soft tissue healing, and underpin a beneficial role of ADSC by regulating inflammation and angiogenesis.

A two-dimensional model based on the expansion of physical wake boundary for wind-turbine wakes

Two-dimensional (2D) wake models with a self-similar Gaussian shape of velocity deficit are highly accurate in predicting wind-turbine wakes. To better leverage their advantages for large-scale engineering applications, an approximation of the physical wake boundary (rw) is proposed based on data from both numerical simulations and experiments, i.e. rw=2σ, where σ is the standard deviation of the Gaussian-like profile. In addition, instead of defining the wake expansion corresponding to σ, a physically more intuitive expansion rate k that corresponds to the physical wake boundary is introduced. Then, a linear expansion law is employed to characterize the evolution of the wake behind the wind rotor, which leaves k as the only parameter to be determined in the 2D wake model. Data from large eddy simulation, physical experiments and field observations shows that the present analytical model can predict the wake of a wind turbine with high accuracy. The cases considered in the present study indicate that k=0.075 recommended by the one-dimensional (1D) wake model (Jensen model) for onshore wind farms also works well in the present 2D model under moderate ground roughness for a turbine generally operating in regime II. Because of its simplicity, good accuracy and low cost, the present 2D model is appealing to large-scale engineering applications.

Static analysis of doubly curved singly ruled truncated FGM cone

In this paper, a new mathematical model for doubly curved singly ruled functionally graded material moderately thick and deep cone is presented. The mathematical model includes a cubic variation of thickness coordinate along with the inclusion of curvature effect in in-plane displacement fields. Due to second degree polynomial transverse shear strain deformation along the thickness of doubly curved singly ruled functionally graded material cone, shear correction factor need is eliminated. The zero-transverse shear strain at upper and lower surface of doubly curved singly ruled functionally graded material cone is imposed in the formulation. The new feature in the present mathematical model is incorporation of normal curvatures in deformation field and twist curvature inclusion in strain expressions. Due to this new feature, the present 2D model can solve problems of moderately thick doubly curved singly ruled functionally graded material cone. The proposed new mathematical model is coded in finite element code and its results are compared with previous published suitable results. After comparison, the present new mathematical model is used to solve many new static problems of doubly curved singly ruled functionally graded material cone considering different volume fraction indices, boundary conditions, geometric parameters.

Modeling of functionally graded sandwich shells accounting for variation in transverse displacement

ABSTRACTIn this study, a simple C0 isoparametric finite element formulation based on higher-order shear deformation theory is presented for static analysis of functionally graded material sandwich shells (FGMSS). To characterize the membrane-flexure behavior observed in a functionally graded shell, a displacement field involving higher-order terms in in-plane and transverse fields is considered. The proposed kinematics field incorporates for transverse normal deformation, transverse shear deformation, and nonlinear variation of the in-plane displacement field through the thickness to predict the overall response of the shell in an accurate sense. To develop the efficient C0 formulation, the derivatives of transverse displacement are treated as independent field variables (nodal unknowns). Voigt's rule of mixture is employed to ascertain the mechanical properties of each layer's constituents along the thickness direction. A wide range of numerical problems are solved assuming various parameters: side-thickness ratio, curvature-side ratio, and gradation parameter, and their interactions with regard to static analysis of FGMSS are discussed in brief. Deflection and stresses incorporating different thickness schemes of sandwich shells are presented in the form of figures. To validate the results, a functionally graded shell without sandwich arrangement is considered. Since no results are available on static analysis of FGMSS, the present 2D model based on the finite element method might be helpful in assessing the applicability of other analytical and numerical models in this area in the future.

Application of 2D numerical model to unsteady performance evaluation of vertical-axis tidal current turbine

Tidal current energy is renewable and sustainable, which is a promising alternative energy resource for the future electricity supply. The straight-bladed vertical-axis turbine is regarded as a useful tool to capture the tidal current energy especially under low-speed conditions. A 2D unsteady numerical model based on Ansys-Fluent 12.0 is established to conduct the numerical simulation, which is validated by the corresponding experimental data. For the unsteady calculations, the SST model, 2×105 and 0.01 s are selected as the proper turbulence model, mesh number, and time step, respectively. Detailed contours of the velocity distributions around the rotor blade foils have been provided for a flow field analysis. The tip speed ratio (TSR) determines the azimuth angle of the appearance of the torque peak, which occurs once for a blade in a single revolution. It is also found that simply increasing the incident flow velocity could not improve the turbine performance accordingly. The peaks of the averaged power and torque coefficients appear at TSRs of 2.1 and 1.8, respectively. Furthermore, several shapes of the duct augmentation are proposed to improve the turbine performance by contracting the flow path gradually from the open mouth of the duct to the rotor. The duct augmentation can significantly enhance the power and torque output. Furthermore, the elliptic shape enables the best performance of the turbine. The numerical results prove the capability of the present 2D model for the unsteady hydrodynamics and an operating performance analysis of the vertical tidal stream turbine.

In vitro experimental models and their molding technology of tumor cell

Traditional cancer researches focus on the analyses of the mice biopsy in order to understand the formation of cancer and the stage of cancer development. In contrast to in vivo experiments, in vitro investigation of cancer cells provides the flexible manipulation of the experimental parameters and the real time observation of the growth and reproduction of cancer cells, thus has been developing rapidly. However, further studies have demonstrated that cells' behavior in a two-dimensional (2D) environment, e.g. Petri dish, is dramatically different from that in a three-dimensional (3D) environment. Therefore, with assistance of bio-microfluidic chips, 3D bio-printing, direct femtosecond laser writing technology and UV curing hydrogel technology, an increasing number of 3D models have been developed to investigate the behaviors of cancer cells in vitro. Nevertheless, the existing technology is also facing the contradiction between accuracy and speed requirements, as well as the biocompatibility and biodegradability of scaffold materials in use. In this paper, we first summarize and compare present 2D models, e. g. Agar Plate and Boyden Assay, and the developing 3D models in vitro experimental approaches as mentioned above, and discuss the merits of these fabricating technologies. Then we focus on the recent progress and achievements of 3D bio-techniques, especially the successful applications in probing the invasion behaviors of cancer cells. Though significant progress has been made from 2D to 3D approaches and these in vitro experimental models are becoming more flawless in simulating the in vivo environment of cells, the following challenges remain: 1) biocompatible material with the appropriate mechanic properties simulating the environment in vivo; 2) the viability of cells in the complex 3D model with of biomaterial, especially during the laser or UV-assisted gelation of hydrogels; 3) the speed and resolution of the present 3D fabrication technologies; 4) the in situ observation and control of cells. Nevertheless, with the development of 3D bio-technologies, breakthroughs can be expected in solving those problems, and thus will guide the 3D experimental models for the invasion of cancer cells in next few years. This will eventually help people in the war towards cancers, and at the same time provide new experimental approaches for other relevant researches in the interdisciplinary fields of biology, physics, chemistry, materials and engineering.

Modelling river bank erosion using a 2D depth-averaged numerical model of flow and non-cohesive, non-uniform sediment transport

Bank erosion can be an important form of morphological adjustment in rivers. With the advances made in computational techniques, two-dimensional (2D) depth-averaged numerical models have become valuable tools for resolving many engineering problems dealing with sediment transport. The objective of this research work is to present a simple, new, bank-erosion operator that is integrated into a 2D Saint-Venant-Exner morphodynamic model. The numerical code is based on an unstructured grid of triangular elements and finite-element algorithms. The slope of each element in the grid is compared to the angle of repose of the bank material. Elements for which the slope is too steep are tilted to bring them to the angle of repose along a horizontal axis defined such that the volume loss above the axis is equal to the volume gain below, thus ensuring mass balance. The model performance is assessed using data from laboratory flume experiments and a scale model of the Old Rhine. For the flume experiment case with uniform bank material, relevant results are obtained for bank geometry changes. For the more challenging case (i.e. scale model of the Old Rhine with non-uniform bank material), the numerical model is capable of reproducing the main features of the bank failure, induced by the newly designed groynes, as well as the transport of the mobilized sediment material downstream. Some deviations between the computed results and measured data are, however, observed. They are ascribed to the effects of three-dimensional (3D) flow structures, pore pressure and cohesion, which are not considered in the present 2D model.

Finite element analysis of laminated composite and sandwich shells using higher order zigzag theory

Static analysis of laminated composite and sandwich shell is presented by developing a C0 finite element (FE) formulation based on higher order zigzag theory (HOZT) using Sander’s approximations. The proposed model satisfies the inter-laminar shear stress continuity at the interfaces; and zero transverse shear stress conditions at shell top and bottom. This is the first finite element implementation of the HOZT to solve the problem of shells incorporating cross curvature effects in shells. The present HOZT predicts transverse shear stresses more accurately than FE results previously published in literature. Numerical results show that the present 2D model is very efficient in predicting the static response of laminated composite and sandwich shallow shell very close to 3D elasticity solutions.

Validation of 1D model for methane/air/Pt combustion in stagnation flow

A 2D model is built on the package of FLUENT to study the effects of radial aspect ratio (R/W), length-to-width ratio (L/W), strain rate (S R), and buoyancy (Ri=Gr/Re 2) on the validation of the simplified 1D model. In the present 2D model, the methane/air homogeneous reaction mechanism of Peters and the methane/air/platinum heterogeneous reaction mechanism of Deutschmann are applied. By comparison between the 1D and 2D numerical results, it is found that the validation of 1D model is highly related with the catalytic stagnation reactor configuration. For length-to-width ratio L/W = 1 configuration, 1D laminar model is applicable when the radial aspect ratio R/W > 0.4. For R/W = 0.6, the reactor exhibited 1D characteristics when L/W < 1. Compared with the temperature and species profiles, the velocity distribution along the axis is more sensitive to the change of radial aspect ratio and length-to-width ratio. With increasing of the strain rate, the flame front goes closer to the catalytic wall surface and the difference between the 1D and 2D results decreases. For a valid 1D simulation, it is recommended that the strain rate should be greater than 20 s-1. The effects of natural convection can be neglected when Ri < 5.

Two-dimensional modeling of subthreshold current and subthreshold swing of double-material-gate (DMG) strained-Si (s-Si) on SGOI MOSFETs

The present paper proposes the surface potential based two-dimensional (2D) analytical models of subthreshold current and subthreshold swing of nanoscale double-material-gate (DMG) strained-Si (s-Si) on Silicon-Germanium-on-Insulator (SGOI) MOSFETs. The surface potential expression has been directly taken from our previous reported work. The effect of various device parameters on subthreshold current and swing like Ge mole fraction, Si film thickness, gate-length ratio and various combinations of control/screen gate work-functions have been discussed. The validity of the present 2D model is verified by using ATLASTM, a 2D device simulator from Silvaco.

Controlled-source marine electromagnetic 2-D modeling gas hydrate studies

Research on gas hydrate has increased recently as an alternative to fossil fuel. This study of marine controlled source electromagnetics (CSEM) is motivated by this increase, particularly in deep waters, and examines representative models. We present 2D models and test their efficacy in detection and characterization of gas hydrates. Earlier modeling studies used a horizontal transmitter to study the CSEM response—two electrical and one magnetic component—for resistive subsurface layers. Here we use six components—three electrical and three magnetic—and show that the proposed method reduces ambiguity in interpretation. Additionally, we show results utilizing the transmitter dipole in a borehole and receivers at the sea bottom. We found that CSEM response from a vertical transmitter helps us characterize resistive layers more confidently than from a transmitter moving horizontally at sea bottom. We conclude that in a complex environment, combining horizontal and vertical movements of the transmitter with sea-bottom receivers helps us delineate the subsurface structure more clearly and may help reduce drilling costs. Our models closely match the gas hydrate region in the Gulf of Mexico—Walker Ridge Block-313. Although this study examines gas hydrate, the methodology is applicable to other areas—for example, in monitoring gas diffusion at subsurface depths, which may help in CO2 sequestration.

On the Boltzmann Equation for 2D Bose-Einstein Particles

This paper considers the spatially homogeneous Boltzmann equation for 2D Bose-Einstein particles. Suppose the collision kernel satisfies some assumptions that include the hard disk model and other possible physical models. We prove the existence of global in time conservative measure solutions of the equation for isotropic initial data, and that for any initial datum which is not totally singular and has positive energy, the solution always converges strongly to the Bose-Einstein distribution as time goes to infinity. This implies that for the present 2D model there is no Bose-Einstein condensation in the sense of long-time limit.

Two-dimensional chiral model for liquid crystals, bent hard needles: A Monte Carlo simulation

The liquid crystalline behavior of a two dimensional (2D) model of hard needles bent into a "zigzag shape" is studied. This model, originally designed to study two dimensional chiral segregation, also shows liquid crystalline behavior and has some anomalous features which are contrasted in relation to the following: (i) Most of the microscopical models used to study liquid crystals have a symmetry axis that coincides with a molecular axis; (ii) in three-dimensions, chiral molecules can form cholesteric instead of nematic phases; (iii) the smectic phase is usually found when attractions are present or at least when the molecules have finite volume. Despite the fact that the present 2D model does not have any of these characteristics, numerical evidence is found for the occurrence of nematic and smectic phases. Since these molecules are athermal, infinitely repulsive, and infinitesimally thin, the liquid crystalline characteristics are attributed to excluded volume effects. To determine the mesophases of the model, both nematic and smectic order parameters as well as distribution functions are computed.