TWO-GRID WEAK GALERKIN METHOD FOR SEMILINEAR ELLIPTIC DIFFERENTIAL EQUATIONS

In this paper, we investigate a two-grid weak Galerkin method for semilinear elliptic differential equations. The method mainly contains two steps. First, we solve the semi-linear elliptic equation on the coarse mesh with mesh size H, then, we use the coarse mesh solution as a initial guess to linearize the semilinear equation on the fine mesh, i.e., on the fine mesh (with mesh size $h$), we only need to solve a linearized system. Theoretical analysis shows that when the exact solution u has sufficient regularity and $h=H^2$, the two-grid weak Galerkin method achieves the same convergence accuracy as weak Galerkin method. Several examples are given to verify the theoretical results.

Synthesis of Spinel-Hydroxyapatite Composite Utilizing Bovine Bone and Beverage Can

Spinel-based hydroxyapatite composite (SHC) has been synthesized utilizing bovine bones as the source of the hydroxyapatite (HAp) and beverage cans as the aluminum (Al) source. The bovine bones were defatted and calcined in the air atmosphere to transform them into hydroxyapatite. The beverage cans were cut and milled to obtain fine Al powder and then sieved to obtain three different particle mesh size fractions: +100#, −140# + 170#, and −170#, or Al particle size of >150, 90–150, and <90 µm, respectively. The SHC was synthesized using the self-propagating intermediate-temperature synthesis (SIS) method at 900 °C for 2 h with (HAp:Al:Mg) ratio of (87:10:3 wt.%) and various compaction pressure of 100, 171, and 200 MPa. It was found that the mechanical properties of the SHC are influenced by the Al particle size and the compaction pressure. Smaller particle size produces the tendency of increasing the hardness and reducing the porosity of the composite. Meanwhile, increasing compaction pressure produces a reduction of the SHC porosity. The increase in the hardness is also observed by increasing the compaction pressure except for the smallest Al particle size (<90 µm), where the hardness instead becomes smaller.

Experimental and Numerical Study on the Protective Behavior of Weldox 900 E Steel Plates Impacted by Blunt-Nosed Projectiles

To demonstrate the importance of incorporating Lode angle into fracture criterion in predicting the penetration resistance of high-strength steel plates, ballistic tests of blunt-nosed projectiles with a diameter of 5.95 mm impacted 4 mm thick Weldox 900 E steel plates were conducted. Impacting velocity range was 136.63~381.42 m/s. The fracture behavior and the ballistic limit velocities (BLVs) were obtained by fitting the initial-residual velocities of the projectiles. Subsequently, axisymmetric finite element (FE) models parallel to the tests were built by using Abaqus/Explicit software, and the Lode-independent Johnson–Cook (JC) and the Lode-dependent ASCE fracture criterion were incorporated into the finite element model for numerical simulation. Meanwhile, to verify the sensitivity of the mesh size in the numerical simulation, different mesh sizes were used in the shear plug area of the target. It can be found that Weldox 900 E steel has obvious mesh size sensitivity by comparing the experimental results and numerical simulation, and the JC fracture criterion and the ASCE fracture criterion predicted similar BLV for the same mesh size.

Liquid Droplet Impact Over Hydrophobic Mesh Surfaces and Assessment of Weber Number Dependent Characteristics

Impacting droplets and droplet ejection from hydrophobic mesh surfaces have interest in biomedicine, heat transfer engineering, and self-cleaning of surfaces. The rate and the size of newborn droplets can vary depending on, the droplet fluid properties, Weber number, mesh geometry, and surface wetting states. In the present study, impacting water droplets onto hydrophobic mesh surface is investigated and impact properties including, spreading, rebounding, and droplet fluid penetration and ejection rates are examined. Droplet behavior is assessed using high recording facilities and predicted in line with the experiments. The findings reveal that the critical Weber number for droplet fluid penetrating/ejecting from mesh screen mainly depends on the droplet fluid capillary length, and hydrophobic mesh size. The contact time of impacting droplet over mesh surface reduces with increasing droplet Weber number, which opposes the case observed for impacting droplets over flat hydrophobic surfaces. The restitution coefficient attains lower values for impacting droplets over mesh surfaces than that of flat surfaces. The rate and diameter of the ejected droplet from the mesh increases as droplet Weber increases. At the onset of impact, streamline curvature is formed inside droplet fluid, which creates a stagnation zone with radially varying pressure at the droplet fluid mesh interface. This reduces the ejected droplet diameter from mesh cells as mesh cells are located away from the impacting vertical axis.

A Space-Time Interior Penalty Discontinuous Galerkin Method for the Wave Equation

A new higher-order accurate space-time discontinuous Galerkin (DG) method using the interior penalty flux and discontinuous basis functions, both in space and in time, is presented and fully analyzed for the second-order scalar wave equation. Special attention is given to the definition of the numerical fluxes since they are crucial for the stability and accuracy of the space-time DG method. The theoretical analysis shows that the DG discretization is stable and converges in a DG-norm on general unstructured and locally refined meshes, including local refinement in time. The space-time interior penalty DG discretization does not have a CFL-type restriction for stability. Optimal order of accuracy is obtained in the DG-norm if the mesh size h and the time step $$\Delta t$$ Δ t satisfy $$h\cong C\Delta t$$ h ≅ C Δ t , with C a positive constant. The optimal order of accuracy of the space-time DG discretization in the DG-norm is confirmed by calculations on several model problems. These calculations also show that for pth-order tensor product basis functions the convergence rate in the $$L^\infty$$ L ∞ and $$L^2$$ L 2 -norms is order $$p+1$$ p + 1 for polynomial orders $$p=1$$ p = 1 and $$p=3$$ p = 3 and order p for polynomial order $$p=2$$ p = 2 .

Sustainable Rigid Polyurethane Foam from Wasted Palm Oil and Water Hyacinth Fiber Composite—A Green Sound-Absorbing Material

A novel rigid sound-absorbing material made from used palm oil-based polyurethane foam (PUF) and water hyacinth fiber (WHF) composite was developed in this research. The NCO index was set at 100, while the WHF content was set at 1%wt with mesh sizes ranging from 80 to 20. The mechanical properties, the morphology, the flammability, and the sound absorption coefficient (SAC) of the PUF composite were all investigated. When the WHF size was reduced from 80 to 20, the compression strength of the PUF increased from 0.33 to 0.47 N/mm2. Furthermore, the use of small fiber size resulted in a smaller pore size of the PUF composite and improved the sound absorption and flammability. A feasible sound-absorbing material was a PUF composite with a WHF mesh size of 80 and an SAC value of 0.92. As a result, PUF derived from both water hyacinth and used palm oil could be a promising green alternative material for sound-absorbing applications.

Adsorption and Sustained Delivery of Small Molecules from Nanosilicate Hydrogel Composites

Two-dimensional nanosilicate particles (NS) have shown promise for the prolonged release of small-molecule therapeutics while minimizing burst release. When incorporated in a hydrogel, the high surface area and charge of NS enable electrostatic adsorption and/or intercalation of therapeutics, providing a lever to localize and control release. However, little is known about the physio-chemical interplay between the hydrogel, NS, and encapsulated small molecules. Here, we fabricated polyethylene glycol (PEG)-NS hydrogels for the release of model small molecules such as acridine orange (AO). We then elucidated the effect of NS concentration, NS/AO incubation time, and the ability of NS to freely associate with AO on hydrogel properties and AO release profiles. Overall, NS incorporation increased the hydrogel stiffness and decreased swelling and mesh size. When individual NS particles were embedded within the hydrogel, a 70-fold decrease in AO release was observed compared to PEG-only hydrogels, due to adsorption of AO onto NS surfaces. When NS was pre-incubated and complexed with AO prior to hydrogel encapsulation, a >9000-fold decrease in AO release was observed due to intercalation of AO between NS layers. Similar results were observed for other small molecules. Our results show the potential for use of these nanocomposite hydrogels for the tunable, long-term release of small molecules.

Distribution and abundance of planktonic mollusks along a longitudinal gradient in the Southeastern Pacific off Chile

The objectives of this research were to estimate the abundance of the main groups of planktonic mollusks (meroplanktonic larvae, holoplanktonic gastropods and cephalopod paralarvae), and relate these groups to the physical-chemical water properties along a longitudinal gradient between Caldera, on the coast of mainland Chile, and the Easter Island ecoregion (Rapa Nui Island and Salas y Gómez Island), in the Southeast Pacific Ocean. Plankton samples were collected over the course of the CIMAR 21-Islas Cruise, from October to November 2015, at 33 oceanographic stations via vertical hauls of a WP2 net (180-µm mesh size) from a maximum depth of 300 m to the sea surface. Mollusks were sorted, counted and initially assigned to Class rank, later being identified to lower taxonomic ranks. Planktonic mollusks were obtained at all stations, and were composed of 92.7% of Gastropoda and 7.3% of Bivalvia. The total abundance of mollusks varied between 55 and 4,922 individuals 100 m-3.Euthecosomate gastropods exhibited the highest occurrence within the oceanic area. Meanwhile, no paralarvae were captured. Differences in the composition of planktonic mollusks between the continental and oceanic zones were evident. Bivalve larvae increased their abundance in warmer, salty and vertically mixed waters. These results are the first record of meroplanktonic mollusks in waters near the Chilean oceanic islands, and suggest that planktonic mollusks display spatial variation at the scale of the South Pacific Basin, which could be related to the hydrographic conditions and the water column structure.