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Fully implicit ADI schemes for solving the nonlinear Poisson-Boltzmann equation

100%

Geng W. , Zhao S.

Molecular Based Mathematical Biology

2013

tom 1

109-123

The Poisson-Boltzmann (PB) model is an effective approach for the electrostatics analysis of solvated biomolecules. The nonlinearity associated with the PB equation is critical when the underlying electrostatic potential is strong, but is extremely difficult to solve numerically. In this paper, we construct two operator splitting alternating direction implicit (ADI) schemes to efficiently and stably solve the nonlinear PB equation in a pseudo-transient continuation approach. The operator splitting framework enables an analytical integration of the nonlinear term that suppresses the nonlinear instability. A standard finite difference scheme weighted by piecewise dielectric constants varying across the molecular surface is employed to discretize the nonhomogeneous diffusion term of the nonlinear PB equation, and yields tridiagonal matrices in the Douglas and Douglas-Rachford type ADI schemes. The proposed time splitting ADI schemes are different from all existing pseudo-transient continuation approaches for solving the classical nonlinear PB equation in the sense that they are fully implicit. In a numerical benchmark example, the steady state solutions of the fully-implicit ADI schemes based on different initial values all converge to the time invariant analytical solution, while those of the explicit Euler and semi-implicit ADI schemes blow up when the magnitude of the initial solution is large. For the solvation analysis in applications to real biomolecules with various sizes, the time stability of the proposed ADI schemes can be maintained even using very large time increments, demonstrating the efficiency and stability of the present methods for biomolecular simulation.

The associations of work style and physical exercise with the risk of work-related musculoskeletal disorders in nurses

61%

Yao Y. , Zhao S. , An Z. , Wang S. , Li H. , Lu L. , Yao S.

tom 32

nr 1

15-24

Objectives This study aimed to investigate the prevalence of work-related musculoskeletal disorders (WMSD) in nurses, and to explore the association of work style and physical exercise with WMSD in this professional group. Material and Methods In this study, a cross-sectional survey design was applied. A questionnaire survey was conducted on 692 nurses in 5 municipal hospitals, in the period August–October 2015. The survey included personal information, lifestyle, physical exercise and symptoms of WMSD. Chi² test and logistic regression were used to identify the risk factors of WMSD. Results The prevalence of WMSD was 84% in all parts of the body in the previous year, with the highest prevalence in the neck (68.2%), followed by waist (67.6%) and shoulder (54.6%). Both univariate and multivariate analyses showed that physical exercise, night shifts and staying up late were associated with WMSD in nurses. The lack of exercise, night shifts and a tendency to stay up significantly increased the risk of WMSD (p < 0.05). Conclusions The prevalence of musculoskeletal disorders among the municipal hospital nursing staff is high. An elevated risk of WMSD is observed in nurses who do not do exercises, work shifts and stay up late. Int J Occup Med Environ Health. 2019;32(1):15–24