A Decoupled and Positivity-Preserving DDFVS Scheme for Diffusion Problems on Polyhedral Meshes

We propose a decoupled and positivity-preserving discrete duality finitevolume (DDFV) scheme for anisotropic diffusion problems on polyhedral meshes withstar-shaped cells and planar faces. Under the generalized DDFV framework, two setsof finite volume (FV) equations are respectively constructed on the dual and primarymeshes, where the ones on the dual mesh are derived from the ingenious combinationof a geometric relationship with the construction of the cell matrix. The resulting system on the dual mesh is symmetric and positive definite, while the one on the primarymesh possesses an M-matrix structure. To guarantee the positivity of the two categories of unknowns, a cutoff technique is introduced. As for the local conservation, itis conditionally maintained on the dual mesh while strictly preserved on the primarymesh. More interesting is that the FV equations on the dual mesh can be solved independently, so that the two sets of FV equations are decoupled. As a result, no nonlineariteration is required for linear problems and a general nonlinear solver could be usedfor nonlinear problems. In addition, we analyze the well-posedness of numerical solutions for linear problems. The properties of the presented scheme are examined bynumerical experiments. The efficiency of the Newton method is also demonstrated bycomparison with those of the fixed-point iteration method and its Anderson acceleration.     

Fully Decoupled,Linear and Unconditionally Energy Stable Schemes for the Binary Fluid-Surfactant Model

Here, we develop a first and a second order time stepping schemes for a binary fluid-surfactant phase field model by using the scalar auxiliary variable approach.The free energy contains a double-well potential, a nonlinear coupling entropy and aFlory-Huggins potential. The resulting coupled system consists of a Cahn-Hilliardtype equation and a Wasserstein type equation which leads to a degenerate problem.By introducing only one scalar auxiliary variable, the system is transformed into anequivalent form so that the nonlinear terms can be treated semi-explicitly. Both theschemes are linear and decoupled, thus they can be solved efficiently. We further provethat these semi-discretized schemes in time are unconditionally energy stable. Somenumerical experiments are performed to validate the accuracy and energy stability ofthe proposed schemes.     

Efficient and Stable Schemes for the Magnetohydrodynamic Potential Model

In this paper, we consider the numerical approximations of a magnetohy-drodynamic potential model that was developed in [15]. Several decoupled, linear, unconditionally energy stable schemes are developed by combining some subtle implicit-explicit treatments for nonlinear coupling terms and the projection-type method for theNavier-Stokes equations. The divergence-free condition for the magnetic field is preserved in the fully-discrete level. We further establish the well-posedness and unconditional energy stabilities of the proposed schemes and present a series of numericalexamples in 3D, including accuracy/stability tests, benchmark simulations of drivencavity flow and hydromagnetic Kelvin-Helmholtz instability.     

Decoupled,Energy Stable Numerical Scheme for the Cahn-Hilliard-Hele-Shaw System with Logarithmic Flory-Huggins Potential

In this paper, a decoupling numerical method for solving Cahn-Hilliard-Hele-Shaw system with logarithmic potential is proposed. Combing with a convex-splitting of the energy functional, the discretization of the Cahn-Hilliard equation intime is presented. The nonlinear term in Cahn-Hilliard equation is decoupled fromthe pressure gradient by using a fractional step method. Therefore, to update the pressure, we just need to solve a Possion equation at each time step by using an incrementalpressure-correction technique for the pressure gradient in Darcy equation. For logarithmic potential, we use the regularization procedure, which make the domain forthe regularized functional $F$($ф$) is extended from (−1,1) to (−∞,∞). Further, the stability and the error estimate of the proposed method are proved. Finally, a series ofnumerical experiments are implemented to illustrate the theoretical analysis.     

On Energy Stable Runge-Kutta Methods for the Water Wave Equation and Its Simplified Non-Local Hyperbolic Model

Although interest in numerical approximations of the water wave equation grows in recent years, the lack of rigorous analysis of its time discretization inhibits the design of more efficient algorithms. In practice of water wave simulations, the trade-off between efficiency and stability has been a challenging problem. Thus to shed light on the stability condition for simulations of water waves, we focus on a model simplified from the water wave equation of infinite depth. This model preserves two main properties of the water wave equation: non-locality and hyperbolicity. For the constant coefficient case, we conduct systematic stability studies of the fully discrete approximation of such systems with the Fourier spectral approximation in space and general Runge-Kutta methods in time. As a result, an optimal time discretization strategy is provided in the form of a modified CFL condition, i.e. $∆t = \mathcal{O}(\sqrt{∆x}).$ Meanwhile, the energy stable property is established for certain explicit Runge-Kutta methods. This CFL condition solves the problem of efficiency and stability: it allows numerical schemes to stay stable while resolves oscillations at the lowest requirement, which only produces acceptable computational load. In the variable coefficient case, the convergence of the semi-discrete approximation of it is presented, which naturally connects to the water wave equation. Analogue of these results for the water wave equation of finite depth is also discussed. To validate these theoretic observation, extensive numerical tests have been performed to verify the stability conditions. Simulations of the simplified hyperbolic model in the high frequency regime and the water wave equation are also provided.     

Optimal advertising and pricing for a three-stage time-lagged monopolistic diffusion model incorporating income

A three-stage time-lagged diffusion model that incorporates consumers' income, advertising and price effects is proposed. The derivation of the model synthesizes and relies upon a number of important arguments made in the diffusion and economic literature. Optimal control theory is used to derive normative advertising and pricing strategic implications for a monopolist introducing a new durable product.     

Hospital Profiling and Hospital Stratification System as a Step for Assessment the Potential of Organ Donation From Deceased Donors

Aim

To be able to calculate the potential of organ donation from deceased donors in a single hospital, region, and country, it is necessary to develop a useful stratification system for all hospitals taking into account their characteristics in having or not having departments crucial for donor identification and recruitment, such as an intensive care unit (ICU or neurology and neurosurgery departments), number of beds, and patient profiles (pediatric vs adult).

Survey for the Opinion of Medical Students and Medical Staff on a Financial Incentive System for Deceased Organ Donation in an Asian Country

BackgroundFinancial incentives for deceased organ donation are associated with many controversial ethical issues. This study examines the perspectives of medical students and staff members on financial incentives for the families of brain-dead organ donors.MethodologyA structured survey form was used between December 7, 2017 and January 28, 2018 to elicit opinions on financial incentives for the families of brain-dead organ donors. Forty-three medical staff members and 81 medical students participated in the survey voluntarily. The opinions on the financial incentive system and the relationship between willingness to give information about organ donation to families and a financial incentive system were assessed.ResultsThe majority of the participants (81.4%) had positive thoughts on organ donation. More than half of the participants (60.5%) thought that the financial incentive system did not erode the ethical purity of organ donation. As charge doctors, most respondents (84.6%) were willing to give information about organ donation to family members in the presence of financial incentives. However, the percentage decreased significantly to 60.5% when financial incentive was no longer factored into consideration (P < .001).LimitationThe study population is small, and the participants are not representative of the general population.ConclusionThe opinions of medical students and medical staff on financial incentives for deceased organ donation were generally positive. Financial incentives proved to be a potential influencing factor as an option of organ donation to be given to families.     

Risk Factors for Peripheral Nerve Injury After 207,000 Total Hip Arthroplasties Using a New York State Database (Statewide Planning and Research Cooperative System)

BackgroundPeripheral nerve injury (PNI) is a devastating complication following total hip arthroplasty (THA). The purpose of this study was to identify risk factors for PNI after THA using a New York Statewide Planning and Research Cooperative System (SPARCS).MethodsThe SPARCS database was queried to identify patients who had undergone THA from 1996 to 2011. Patient demographics, medical history, surgical details, hospital characteristics, and in-hospital complications were recorded. Cases in which a new unilateral PNI was identified were compiled, as were control cases in which a new PNI did not occur. The characteristics of cases and controls underwent univariate testing and a multivariate logistic regression using Akaike information criterion model selection to identify risk factors for the development of PNI after THA.Results207,981 cases were identified, and 487 were coded as having a new PNI. Preexisting spinal conditions (odds ratio [OR] = 2.55, confidence interval [CI] = 1.61-3.83) were strongly correlated with the development of PNI postoperatively, as was dislocation (OR = 2.58, CI = 1.01-5.30) and diabetes with chronic complications (OR = 2.26, CI = 0.96-4.43). Younger age, in-hospital complications, and thromboembolic events were also associated with postoperative PNI.ConclusionThe incidence of PNI after THA was consistent with previous large-scale studies but may under-represent the true incidence because of undercoding inherent in large database studies. Previous spine disorder, chronic diabetes, younger age, and in-hospital postoperative complications all increased the risk of PNI. This study can help health-care providers and systems identify patients at higher risk of this serious complication.