Numerical Boundary Research Articles

Elastic films of single-crystal two-dimensional covalent organic frameworks.

The properties of polycrystalline materials are often dominated by defects; two-dimensional (2D) crystals can even be divided and disrupted by a line defect1-3. However, 2D crystals are often required to be processed into films, which are inevitably polycrystalline and contain numerous grain boundaries, and therefore are brittle and fragile, hindering application in flexible electronics, optoelectronics and separation1-4. Moreover, similar to glass, wood and plastics, they suffer from trade-off effects between mechanical strength and toughness5,6. Here we report a method to produce highly strong, tough and elastic films of an emerging class of 2D crystals: 2D covalent organic frameworks (COFs) composed of single-crystal domains connected by an interwoven grain boundary on water surface using an aliphatic bi-amine as a sacrificial go-between. Films of two 2D COFs have been demonstrated, which show Young's moduli and breaking strengths of 56.7 ± 7.4 GPa and 73.4 ± 11.6 GPa, and 82.2 ± 9.1 N m-1 and 29.5 ± 7.2 N m-1, respectively. We predict that the sacrificial go-between guided synthesis method and the interwoven grain boundary will inspire grain boundary engineering of various polycrystalline materials, endowing them with new properties, enhancing their current applications and paving the way for new applications.

High order compact augmented methods for Stokes equations with different boundary conditions

This paper is devoted to fourth order compact schemes and fast algorithms for solving stationary Stokes equations with different boundary conditions numerically. One of the main ideas is to decouple the Stokes equations into three Poisson equations for the pressure and the velocity via the pressure Poisson equation (PPE). The augmented strategy is utilized to provide numerical boundary conditions for the pressure. Different velocity boundary conditions require different interpolation strategies for the augmented methods. The augmented variable is solved by the GMRES method. A new simple and efficient preconditioning strategy has also been developed to accelerate the convergence of the GMRES iteration. Numerical examples presented in this paper confirmed the designed convergence order and the efficiency of the new methods.

Insight into the dynamics of bioconvective Walter’s-B nanofluid flow subjected to Cattaneo–Christov heat flux and activation energy

In order to study the implementation of the generalized magnetohydrodynamic (MHD) bioconvective aspects of the Walter’s-B fluid flows over a convectively heated stretched sheet in the presence of activation energy and numerous boundary conditions, the non-homogeneous nanofluid flow model is used. Here, the nonlinear differential equations illustrating the current nanofluid flow model of non-Newtonian fluid explicitly include the concentration of both motile microbes and solid nanoparticles. Furthermore, the associated temperature, impact of thermal radiation and the Cattaneo–Christov heat flux model are discussed. The similarity transformations are formally displayed to transfer the consequential reduction in the mathematical complexity of the existing physical situation by converting partial differential equations (PDEs) into a nonlinear associated framework of ordinary differential equations (ODEs). Furthermore, the homotopy analysis method (HAM) through the MATLAB tool is used to numerically solve the dimensionless similarity equations. The results are extremely well demonstrated. In this manner, the significant engineering procedures are more accurately and entirely estimated before being reported. The results of the fixed physical factors of velocity, temperature, concentration, and microbe concentration profiles are effectively demonstrated through multiple types of illustrations and comprehensive explanations. The principal assumption is that the greater significance of the bioconvection Lewis and Peclet numbers can lead to a drop in the microbe concentration profile. It is observed that the concentration profile is reduced with the greater value of the concentration relaxation parameter.

Microstructural evolution and mechanical properties of pure zinc subjected to extrusion and caliber rolling

This study investigates the microstructural evolution and mechanical properties of pure zinc (Zn) during extrusion and multi-pass caliber rolling (CR). Electron backscatter diffraction (EBSD) and transmission electron microscopy (TEM) analyses indicate that plastic deformation induces dynamic recrystallization (DRX), resulting in the formation of numerous low angle grain boundaries (LAGBs) and substructures. In particular, significant grain refinement (∼1.6 μm) is achieved with the texture deviating 30 ± 5° from the <0001> direction. The as-extruded pure Zn exhibits a yield strength (YS) of 130 MPa, an ultimate tensile strength (UTS) of 151 MPa, and an elongation (EL.) of 8.8 %, respectively. Subsequent caliber rolling significantly improved these mechanical properties (i.e., YS: 225 MPa; UTS: 301 MPa; EL.: 31%) due to the combined effect of grain refinement, dislocations and texture strengthening. In addition, the deformation mechanism shifts from an initial influence of both dislocations and twins to a predominance of dislocations alone.

Vector form intrinsic finite element analysis for nonlinear parametric resonances of planar beam structures

The parametric resonance of a beam structure may lead to a disastrous consequence. To assess the safety of a structure, structural engineers need a straightforward and practical method to calculate the large-amplitude nonlinear parametric resonance responses of the beam structure. This paper proposes a newly developed vector form intrinsic finite element (VFIFE) calculation scheme to analyse the nonlinear parametric resonance of planar beam structures. By taking into account the geometric stiffness effect of the internal axial force for the frame element, a new relationship between internal nodal forces and deformation components is first established based on the VFIFE principle and the parametric resonance mechanism of frame structures. A numerical example of a portal frame is presented to demonstrate the efficacy of this new calculation scheme. A parametric resonance test of the cantilever beam is conducted to verify the applicability of the VFIFE method. The numerical results show that the proposed scheme can well simulate the nonlinear phenomena of parametric resonances. The numerical predictions are consistent with the experimental observations. A filtering-based finite-time Lyapunov exponent approach is presented to determine the stability boundary of the structure. The numerical stability boundary of parametric resonance agrees well with the experimental boundary. Possible causes of deviations between the numerical and experimental results are discussed. The proposed VFIFE scheme is a simple and effective means of analysing the stability and nonlinear responses of the parametric resonance of planar beam structures.

Cut-PFEM: a Particle Finite Element Method using unfitted boundary meshes

AbstractIn this work, we present a novel unfitted mesh boundary strategy in the context of the Particle Finite Flement Method (PFEM) aiming to improve endemic limitations of the PFEM relative to boundary conditions treatment and mass conservation. In this new methodology, which we called Cut-PFEM, the fluid–wall interaction is not performed by adding interface elements, as is done in the standard PFEM boundaries. Instead, we use an implicit representation of (all or some of) the boundaries by introducing the use of a level set function. Such distance function detects the elements trespassing the (virtual) contours of the domain to equip them with opportunely boundary conditions, which are variationally enforced using Nitsche’s method. The proposed Cut-PFEM circumvents important issues associated with the standard PFEM contact detection algorithm, such as the artificial addition of mass to the computational domain and the anticipation of contact time. Furthermore, the Cut-PFEM represents a natural ground for the imposition of alternative wall boundary conditions (e.g., pure slip) which pose significant difficulties in a standard PFEM framework. Several numerical examples, featuring both no-slip and slip boundary conditions, are presented to prove the accuracy and robustness of the method in two-dimensional and three-dimensional scenarios.

Friction in Rolling a Cylinder on or Under a Viscoelastic Substrate with Adhesion

In classical experiments, it has been found that a rigid cylinder can roll both on and under an inclined rubber plane with a friction force that depends on a power law of velocity, independent of the sign of the normal force. Further, contact area increases significantly with velocity with a related power law. We try to model qualitatively these experiments with a numerical boundary element solution with a standard linear solid and we find for sufficiently large Maugis–Tabor parameter λ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\lambda$$\\end{document} qualitative agreement with experiments. However, friction force increases linearly with velocity at low velocities (like in the case with no adhesive hysteresis) and then decays at large speeds. Quantitative agreement with the Persson–Brener theory of crack propagation is found for the two power law regimes, but when Maugis–Tabor parameter λ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\lambda$$\\end{document} is small, the cut-off stress in Persson–Brener theory depends on all the other dimensionless parameters of the problem.

Laser cleaning for inorganic thermal control coatings on aluminum alloys: Microstructure evolution and mechanical properties of substrate

Thermal control coatings are crucial materials in spacecraft thermal protection systems. Investigating efficient, convenient, and environmentally friendly removal techniques for thermal control coatings is essential for their application and development. This study developed a new removal technology for thermal control coatings using nanosecond pulse laser cleaning technology. The removal effect of the thermal control coating was studied, and the microstructure evolution and mechanical properties of the substrate were analyzed. The results showed that the coating was completely removed at 5.73 and 7.00 J/cm2, while at 8.28 J/cm2, in addition to the coating, approximately 5±1.1 μm of the substrate was also removed. In the completely cleaned state, micro-melting occurred on the substrate surface, and nanostructures appeared. At 5.73 and 7.00 J/cm2, the thickness of the remelted layer is 4±0.9 μm and 5.5±0.6 μm, respectively. The grains in the remelted layer exhibit significant refinement, accompanied by the observation of numerous subgrain boundaries. Additionally, the substrate surface exhibits tensile residual stress after laser cleaning. Attributed to the influence of the remelted layer, the surface hardness and tensile properties of the substrate are slightly improved after laser cleaning compared to manual grinding.

A Study of Electroplated Nanoporous Copper Using Aberration-Corrected Transmission Electron Microscopy.

Nanoporous Cu foam is widely applied in many fields such as the packaging of electronic power devices. In this study, a sandwich-structured Cu-Zn eutectic alloy precursor composed of Cu0.53Zn0.47/Cu5Zn8/Cu0.53Zn0.47 is prepared through electroplating. The surface layer of the precursor, Cu0.53Zn0.47, has a flat surface with numerous grain boundaries, which effectively promotes its dealloying behavior. By contrast, Cu5Zn8 has a porous structure, which promotes the dealloying behavior at the center of the precursor. The dealloying of Cu0.53Zn0.47 is dominated by the coherent surface diffusion of Cu atoms, and the crystal lattice and orientation show no changes before and after dealloying. By contrast, the dealloying behavior of Cu5Zn8 requires the renucleation of Cu crystals; in this process, Cu atoms are transported to the surface of the layer by capillary forces to form clusters, which nucleate and grow.

A new method to suppress reflections from numerical boundaries in wave propagation

A new method to suppress reflections from numerical boundaries in wave propagation

Vital sign measurements demonstrate terminal digit bias and boundary effects.

The measurement and recording of vital signs may be impacted by biases, including preferences for even and round numbers. However, other biases, such as variation due to defined numerical boundaries (also known as boundary effects), may be present in vital signs data and have not yet been investigated in a medical setting. We aimed to assess vital signs data for such biases. These parameters are clinically significant as they influence care escalation. Vital signs data (heart rate, respiratory rate, oxygen saturation and systolic blood pressure) were collected from a tertiary hospital electronic medical record over a 2-year period. These data were analysed using polynomial regression with additional terms to assess for underreporting of out-of-range observations and overreporting numbers with terminal digits of 0 (round numbers), 2 (even numbers) and 5. It was found that heart rate, oxygen saturation and systolic blood pressure demonstrated 'boundary effects', with values inside the 'normal' range disproportionately more likely to be recorded. Even number bias was observed in systolic heart rate, respiratory rate and blood pressure. Preference for multiples of 5 was observed for heart rate and blood pressure. Independent overrepresentation of multiples of 10 was demonstrated in heart rate data. Although often considered objective, vital signs data are affected by bias. These biases may impact the care patients receive. Additionally, it may have implications for creating and training machine learning models that utilise vital signs data.

Guanidinium‐Based Manganese(II) Bromide with High Glass‐Forming Ability for Thermoplastic Curved X‐ray Imaging

AbstractThe development of large‐area transparent organic‐inorganic hybrid metal halide (OIMH) scintillation screens is restricted by the anisotropic single‐crystal growth, numerous grain boundaries in polycrystalline wafers, and inhomogeneous dispersion in perovskite‐polymer composite films. The crystal‐glass phase transition of OIMH materials may provide a promising solution for the above significant challenges. Herein, a new class of transparent amorphous guanidinium‐based manganese bromide glasses, (DPG)2MnBr4 and (DOTG)2MnBr4 (DPG = 1,3‐diphenylguanidinium, DOTG = 1,3‐di‐o‐tolylguanidinium), are synthesized through a low‐temperature melt‐quenching process. The (DOTG)2MnBr4 shows impressive glass‐forming ability because of large viscosity (η) at the melting temperature (Tm) (η(Tm) = 3426 mPa·s) and small fragility index (m = 52.35), which can be a potential glass scintillator. The large‐area (e.g., 13 cm × 13 cm) transparent amorphous (DOTG)2MnBr4 glass scintillator shows high light transmittance of &gt; 80%, a low detection limit of 237.3 nGy s−1 and high X‐ray imaging spatial resolution of 12 lp mm−1. Interestingly, the glass transition temperature of &lt; 40 °C gives (DOTG)2MnBr4 glass unique thermoplastic properties, allowing it to conform to irregularly shaped objects and reduce the distortion in X‐ray imaging.

Simulating the Photospheric to Coronal Plasma Using Magnetohydrodynamic Characteristics. I. Data-driven Boundary Conditions

We develop a general description of how information propagates through a magnetohydrodynamic (MHD) system based on the method of characteristics and use that to formulate numerical boundary conditions that are intrinsically consistent with the MHD equations. Our formulation includes two major advances for simulations of the Sun. First, we derive data-driven boundary conditions that optimally match the state of the plasma inferred from a time series of observations of a boundary (e.g., the solar photosphere). Second, our method directly handles random noise and systematic bias in the observations, and finds a solution for the boundary evolution that is strictly consistent with MHD and maximally consistent with the observations. We validate the method against a Ground Truth (GT) simulation of an expanding spheromak. The data-driven simulation can reproduce the GT simulation above the photosphere with high fidelity when driven at high cadence. Errors progressively increase for lower driving cadence until a threshold cadence is reached and the driven simulation can no longer accurately reproduce the GT simulation. However, our characteristic formulation of the boundary conditions still requires adherence of the boundary evolution to the MHD equations even when the driven solution departs from the true solution in the driving layer. That increasing departure clearly indicates when additional information at the boundary is needed to fully specify the correct evolution of the system. The method functions even when no information about the evolution of some variables on the lower boundary is available, albeit with a further decrease in fidelity.

Estimating water transport in carbon nanotubes: a critical review and inclusion of scale effects.

The quasi-frictionless water flow across graphitic surfaces offers vast opportunities for a wide range of applications from biomedical science to energy. However, the conflicting experimental results impede a clear understanding of the transport mechanism and desired flow control. Existing literature proposes numerous modifications and updated boundary conditions to extend classical hydrodynamic theories for nanoflows, yet a consensus or definitive conclusion remains elusive. This study presents a critical review of the proposed modifications of the pressure driven flow or the Hagen-Poiseuille (HP) equations to estimate the flow enhancement through carbon nanotubes (CNTs). For such a case, we performed (semi-)classical molecular dynamics simulations of water flow in various sizes of CNTs, applied the different forms of boundary definitions from the literature, and derived HP equation models by implementing these modifications. By aggregating seven distinct experimental datasets, we tested various flow enhancement models against our measurements. Our findings indicate that including the interfacial layering-based dynamic slip-definition in the proposed HP equations yields accurate estimations. While considering interfacial viscosity predicts the individual CNT experiments well, using the experimental viscosity yields better estimations of measurements for the water flow enhancement through membranes of CNTs. This critical review testing existing literature demonstrates how to refine continuum fluid mechanics to predict water flow enhancement at the nanoscale providing holistic multiscale modeling.

High strength and ductility in a new Mg–Zn–Ga biocompatible alloy by drawing and rotary forging

A comparative study of the effect of drawing and rotary forging on the structure, mechanical and corrosion properties of a new biodegradable magnesium alloy Mg–2Zn–2Ga was carried out. The original 6 mm diameter bars obtained by hot extrusion were reduced to the diameters in the range 5.5–3.3 mm by drawing or rotary forging. Optical microscopy, scanning electron microscopy and EBSD grain orientation mapping were used to characterize the material microstructure. Tensile testing was performed to determine the mechanical properties. The optimum temperature for rotary forging and annealing after each drawing pass for defect-free bar production was found to be 300 °C. The combination of the highest strength and ductility was achieved in the 4.2 mm diameter drawn bar and is explained by the formation of numerous twin boundaries in the alloy structure. The 3.3 mm diameter bar obtained by drawing as well as the 5.5 mm diameter bar obtained by rotary forging showed a balance between high strength (260–310 MPa) and large elongation (9–12 %). The analysis of the stress-strain curves using Hollomon's equation was conducted. The hydrogen evolution test in Hanks' solution revealed that the drawn bars of diameters 4.2 and 5.2 mm, as well as the rotary forged bar of 5.5 mm possessed 3 times lower corrosion resistance reduced in comparison with the original 6 mm extruded bar. The 3.3 mm diameter drawn bar exhibited the lowest nominal corrosion rate of 0.11 mm/year that offers excellent opportunities for use in medical implants.

Hans Namuth’s Photographs and Film Studies of Jackson Pollock: Transforming American Postwar Avant-Garde Labor into Popular Consumer Spectacle

Abstract Expressionism is often regarded as the first purely American art movement and the first to gain mass cultural recognition. Prior to the 1940s, the consideration and appreciation of abstract art belonged to a certain intellectual elite, but the intimidating complexity of Abstract Expressionism, the daring allure of its artists, and the particularities of mid-century American culture converged to transform the avant-garde into consumer spectacle. This shift represented, and was symptomatic of, a larger societal rearrangement: information and commodity superseded industrialized labor as the core of American culture. Jackson Pollock, America’s first avant-garde superstar, stood at the center of this shift, at once representing both active creative labor and the commodification of the idea of that labor. Hans Namuth’s photographs and films of Pollock placed him and his art firmly in the realm of consumable popular spectacle, underlying further connections to Hollywood film and prominent print media. This article examines how Pollock became a paradigmatic figure in the avant-garde’s proliferation into mass culture and asserts that mass culture did not simply subsume the avant-garde. Rather, the two realms engaged in a mutual construction that pushed the avant-garde across numerous social boundaries. The artistic, critical, and popular receptions that grew out of this convergence erased distinctions between ‘high’ and ‘low’ culture.

ALD-Based Interface Engineering for Improving Electrical Conductivity of Nanoporous Thermoelectric Materials

The way to improve the performance of thermoelectric materials is to break the strong correlation between electrical conductivity and thermal conductivity. Combining porous structures with atomic layer deposition (ALD) is a promising strategy to solve this problem. The porous structure introduced into thermoelectric materials effectively lowers the lattice thermal conductivity, greatly increasing performance. However, the formation of nanopores is accompanied by a decrease in electrical conductivity. Here, we create nanoporous Bi0.4Sb1.6Te3 powder formed through selective dissolution from the mixture of KCl and Bi0.4Sb1.6Te3 powder. We propose a strategy to control carrier concentration by ALD of ZnO on nanoporous Bi0.4Sb1.6Te3 powder, thereby improving electrical conductivity and lowering thermal conductivity. Even after spark plasma sintering, ZnO is conformally formed at the nanoporous Bi0.4Sb1.6Te3 grain boundaries. The electrical conductivity increases from 651.72 S/cm to 724.52 S/cm by interfacial reaction of ZnO and Bi0.4Sb1.6Te3. In addition, ZnO inhibits grain growth and creates numerous grain boundaries to lower the lattice thermal conductivity of the porous structure. As a result, the ZT of the nanoporous Bi0.4Sb1.6Te3 deposited with ZnO is increased by 46%. This study demonstrates that ALD is an effective method for improving the conductivity of nanoporous thermoelectric materials.

Heat and mass transfer phenomenon and aligned entropy generation with simultaneous effect for magnetized ternary nanoparticles induced by ferro and nano-layer fluid flow of porous disk subject to motile microorganisms

This articles focus the dynamics of fluid conveying ternary solid particles, nano-layer, and magnetic field effects subject to porous disks. The magnetized ternary nanoparticles induced by Ferro and nano-layer are considered due to their unusual characteristics like extraordinary thermal conductivity, which are significant in advanced nanotechnology, heat exchangers, material sciences, and electronics. To avoid possible sedimentation of tiny particles, the motile microorganisms are also considered in the elaborated fluid problem. The main objective of this comprehensive study is the enhancement of heat transportation. In this study, we also investigate the physical dynamics of entropy generation, particularly emphasizing viscous dissipation related to joule heating effects. The mass transfer equation was employed to monitor the chemical interaction with diverse nanoparticles. The results of comparative and numerical validation agree well. The approach of stable and accurate numerical boundary value problem of fourth order code (bvp4c) is applied to solve the nonlinear system of ordinary differential equations. Many useful engineering results are summarized here, including the skin friction coefficient ( C f ) , Nusselt number (Nu), Sherwood number (Sh), and motile number (Nn). For both porous disks, several non-dimensional parameter effects are depicted graphically and tabulated. The results show that the increasing the number of nanolayer particles slows the rate of the temperature profile in both porous disks, associated with the expansion ratio, Reynolds number, and magnetic field number. Moreover, increasing the values of the density ratio number results in an increase in the flow of microorganisms profile in both porous disks. Increasing the values of the diffusivity parameters and the temperature difference enhances the flow of entropy generation.

The Simulation of The Propagation of Electromagnetic Waves Through a Material with Various Thicknesses Using Finite Difference Time Domain (FDTD)

A finite difference time domain method in one dimension (1D-FDTD) is employed to study the properties of the propagation of electromagnetic waves across a medium with finite thicknesses. In this paper, we simulated the propagation of a Gaussian pulse. Since we simulated in one dimension, the absorbing boundary condition (ABC) can be applied to minimize undesirable reflection which generated at the numerical boundaries. We also implemented total field / scattering field (TF/SF) to ensure the source propagated in only one direction. The analysis performed by inserting the object with both relative permittivity and permeability values higher than one decreased the pulse’s amplitude.

Error estimates for a viscosity-splitting scheme in time applied to non-Newtonian fluid flows

A time fractional-step method is presented for numerical solutions of the incompressible non-Newtonian fluids for which the viscosity is non-linear depending on the shear-rate magnitude according to a generic model. The method belongs to a class of viscosity-splitting procedures and it consists of separating the convection term and incompressibility constraint into two time steps. Unlike the conventional projection methods, the viscosity is not dropped in the last step allowing to enforce the full original boundary conditions on the end-of-step velocity which eliminates any concerns about the numerical boundary layers. We carry out a rigorous error analysis and provide a full first-order error estimate for both the velocity and pressure solutions in the relevant norms. Numerical results are presented for two test examples of non-Newtonian fluid flows to demonstrate the theoretical analysis and confirm the reliability of this viscosity-splitting scheme.