Large gatherings of people on cruise ships and warships are often at high risk of COVID-19 infections. To assess the transmissibility of SARS-CoV-2 on warships and cruise ships and to quantify the effectiveness of the containment measures, the transmission coefficient (β), basic reproductive number (R0), and time to deploy containment measures were estimated by the Bayesian Susceptible-Exposed-Infected-Recovered model. A meta-analysis was conducted to predict vaccine protection with or without non-pharmaceutical interventions (NPIs). The analysis showed that implementing NPIs during voyages could reduce the transmission coefficients of SARS-CoV-2 by 50%. Two weeks into the voyage of a cruise that begins with 1 infected passenger out of a total of 3,711 passengers, we estimate there would be 45 (95% CI:25-71), 33 (95% CI:20-52), 18 (95% CI:11-26), 9 (95% CI:6-12), 4 (95% CI:3-5), and 2 (95% CI:2-2) final cases under 0%, 10%, 30%, 50%, 70%, and 90% vaccine protection, respectively, without NPIs. The timeliness of strict NPIs along with implementing strict quarantine and isolation measures is imperative to contain COVID-19 cases in cruise ships. The spread of COVID-19 on ships was predicted to be limited in scenarios corresponding to at least 70% protection from prior vaccination, across all passengers and crew.

If the closed wire frame of a soap film having the shape of a Möbius strip is pulled apart and gradually deformed into a planar circle, the soap film transforms into a two-sided orientable surface. In the presence of a finite-time twist singularity, which changes the linking number of the film's Plateau border and the centreline of the wire, the topological transformation involves the collapse of the film toward the wire. In contrast to experimental studies of this process reported elsewhere, we use a numerical approach based on the immersed boundary method, which treats the soap film as a massless membrane in a Navier-Stokes fluid. In addition to known effects, we discover vibrating motions of the film arising after the topological change is completed, similar to the vibration of a circular membrane.

In this paper, we propose a new energy-preserving scheme and a new momentum-preserving scheme for the modified regularized long wave equation. The proposed schemes are designed by using the discrete variational derivative method and the finite volume element method. For comparison, we also propose a finite volume element scheme. The conservation properties of the proposed schemes are analyzed and we find that the energy-preserving scheme can precisely conserve the discrete total mass and total energy, the momentum-preserving scheme can precisely conserve the discrete total mass and total momentum, while the finite volume element scheme merely conserve the discrete total mass. We also analyze their linear stability property using the Von Neumann theory and find that the proposed schemes are unconditionally linear stable. Finally, we present some numerical examples to illustrate the effectiveness of the proposed schemes.

In this paper, a numerical method is presented for simulating the 3D interfacial flows with insoluble surfactant. The numerical scheme consists of a 3D immersed interface method (IIM) for solving Stokes equations with jumps across the interface and a 3D level-set method for solving the surfactant convection-diffusion equation along a moving and deforming interface. The 3D IIM Poisson solver modifies the one in the literature by assuming that the jump conditions of the solution and the flux are implicitly given at the grid points in a small neighborhood of the interface. This assumption is convenient in conjunction with the level-set techniques. It allows standard Lagrangian interpolation for quantities at the projection points on the interface. The interface jump relations are re-derived accordingly. A novel rotational procedure is given to generate smooth local coordinate systems and make effective interpolation. Numerical examples demonstrate that the IIM Poisson solver and the Stokes solver achieve second-order accuracy. A 3D drop with insoluble surfactant under shear flow is investigated numerically by studying the influences of different physical parameters on the drop deformation.

We develop an unconditionally energy stable immersed boundary method, and apply it to simulate 2D vesicle dynamics. We adopt a semi-implicit boundary forcing approach, where the stretching factor used in the forcing term can be computed from the derived evolutional equation. By using the projection method to solve the fluid equations, the pressure is decoupled and we have a symmetric positive definite system that can be solved efficiently. The method can be shown to be unconditionally stable, in the sense that the total energy is decreasing. A resulting modification benefits from this improved numerical stability, as the time step size can be significantly increased (the severe time step restriction in an explicit boundary forcing scheme is avoided). As an application, we use our scheme to simulate vesicle dynamics in Navier-Stokes flow.

We extend the immersed boundary (IB) method to simulate the dynamics of a 2D dry foam by including the topological changes of the bubble network. In the article [Y. Kim, M.-C. Lai, and C. S. Peskin, J. Comput. Phys. 229:5194-5207,2010], we implemented an IB method for the foam problem in the two-dimensional case, and tested it by verifying the von Neumann relation which governs the coarsening of a two-dimensional dry foam. However, the method implemented in that article had an important limitation; we did not allow for the resolution of quadruple or higher order junctions into triple junctions. A total shrinkage of a bubble with more than four edges generates a quadruple or higher order junction. In reality, a higher order junction is unstable and resolves itself into triple junctions. We here extend the methodology previously introduced by allowing topological changes, and we illustrate the significance of such topological changes by comparing the behaviors of foams in which topological changes are allowed to those in which they are not.

We studied the polarization-dependent photoluminescence (PL) of a-plane GaN /AlGaN multiple quantum wells (MQWs) grown on r-plane sapphire substrate with the various well width from 1.5 to 7.33 nm. To clarify the reasons of light emission polarization properties, we applied the 6×6 k‧p model to simulate the E-k dispersion relation and the wave functions to obtain the polarization optical transitions. According to the experimental result, the PL emission peak position exhibits a red-shifted with increasing well width, due to the reduction of the quantum confinement effect. The polarization ratio of a-plane GaN/AlGaN MQWs increased from 0.236 to 0.274 with increasing the quantum well width. This phenomenon is believed to be that y-polarized light emission gradually dominates the PL spectrum and thus enhances the polarization ratio.

In this paper, new finite difference methods based on the augmented immersed interface method (IIM) are proposed for simulating an inextensible moving interface in an incompressible two-dimensional flow. The mathematical models arise from studying the deformation of red blood cells in mathematical biology. The governing equations are incompressible Stokes or Navier-Stokes equations with an unknown surface tension, which should be determined in such a way that the surface divergence of the velocity is zero along the interface. Thus, the area enclosed by the interface and the total length of the interface should be conserved during the evolution process. Because of the nonlinear and coupling nature of the problem, direct discretization by applying the immersed boundary or immersed interface method yields complex nonlinear systems to be solved. In our new methods, we treat the unknown surface tension as an augmented variable so that the augmented IIM can be applied. Since finding the unknown surface tension is essentially an inverse problem that is sensitive to perturbations, our regularization strategy is to introduce a controlled tangential force along the interface, which leads to a least squares problem. For Stokes equations, the forward solver at one time level involves solving three Poisson equations with an interface. For Navier-Stokes equations, we propose a modified projection method that can enforce the pressure jump condition corresponding directly to the unknown surface tension. Several numerical experiments show good agreement with other results in the literature and reveal some interesting phenomena.

Synthesis and characterization of a new carbon particle are investigated in this study. The carbon particle, which possesses a very high surface area (682 cm2/g), is suitable for catalysts loading in application of fuel cell. As well known, carbon materials are used to be a support of Pt catalyst to achieve high dispersion to enhance the activity of Pt. The synthesis was performed by conventional arc discharge process between two graphite electrodes in vacuum. A high-current range from 100∼ 300 ampere was utilized to evaporate the cathode electrode in order to produce carbon soot onto the wall of chamber, and further high production rate of 10 g/hr was achieved. The morphology and microstructure of the materials were investigated by SEM, HRTEM, XRD and Raman spectroscopy.

Observations of the soot by SEM and HRTEM have shown that it consists agglomerations of carbon particles linked each other to form a chain-like structure. Most carbon particles are approximate 30 ∼ 60 nm in diameter. HRTEM observation reveals that a carbon particle is comprised of several defective onions with different diameters and extremely curled graphene sheets, which appear as double-sheet layers.

The microstructure and field emission properties of multi walled carbon nanotubes (MWNTs) were investigated. The comparisons are made between MWNTs synthesized by high temperature arc methods and low temperature CVD methods. The results of the HRTEM image clearly exhibit characteristic features of a multi walled carbon nanotube. Raman spectrum shows a stronger peak at about 1580 cm-1 indicating the formation of a well-graphitized carbon nanotube. It also shows the high temperature arc process can produce MWNT that has perfect graphitic layer structure and high I(G)/I(D) ratio. The Ratio of G-line (sp2 bond) and D-line(sp3 bond) of these MWNTs are about 2.8 to 5.2. From the field emission measurement, the low onset field is about 1.4 to 2.4 V/ m, and can be attributed to highly sharp tips and high electric conductivity of MWNTs.