Workplace violence against Chinese health professionals 2013-2021: A study of national criminal judgment documents.

Objectives: Patient-initiated hospital violence is a global problem which threatens the safety of health professionals and is indicative of doctor-patient tensions, impeding health system quality and access. The current study aimed to improve the understanding of medical workplace violence (WPV) in China, using authoritative and nationally representative judgment records, and to approach violence prevention strategies. Methods: All litigation records relating to violence against health professionals between 2013 and 2021 were extracted from the China Judgment Online System. Basic case information, victim characteristics, perpetrator characteristics and the nature of the violence were collated. The relationship between different treatment outcomes and violence was also explored. Results: Numbers of cases of hospital violence gradually increased from 2013 to a peak in 2016 before gradually decreasing in the following years. The most common perpetrators were patients' relatives (58.2%), followed by patients themselves (38.2%). Only 9 perpetrators had a confirmed history of mental illness and only two were intoxicated with alcohol. More than half of the cases (52.5%) occurred in rural areas and this percentage is even greater for primary health care institutions (71.4%) and secondary hospitals (73.5%). On a departmental level, the highest incidence of medical WPV was found in the emergency (18.9%), pediatrics (13.2%) and obstetrics (11.5%) departments. Violent behaviors, such as stalking, mass occupation of the ward and sharp instrument injury were significantly related to cases not involving patient death (p < 0.05). Disruptive behavior, such as hanging banners, blocking hospital passages, placing flower wreaths and burning paper money were significantly correlated with cases involving patient death (p < 0.01). The interval between a patient's death and the ensuing violence was short, happening on the same day in 54.8% of cases. Conclusions: A comprehensive overview of medical WPV in China is presented and may have utility for the formulation of prevention strategies.

Evaluation of Abramowitz functions in the right half of the complex plane.

A numerical scheme is developed for the evaluation of Abramowitz functions Jn in the right half of the complex plane. For n = - 1, … , 2, the scheme utilizes series expansions for ∣z∣ < 1, asymptotic expansions for ∣z∣ > R with R determined by the required precision, and least squares Laurent polynomial approximations on each sub-region in the intermediate region 1 ≤ ∣z∣ ≤ R. For n > 2, Jn is evaluated via a forward recurrence relation. The scheme achieves nearly machine precision for n = -1, … , 2 at a cost that is competitive as compared with software packages for the evaluation of other special functions in the complex domain.

Theory of the Lattice Boltzmann method: Derivation of macroscopic equations via the Maxwell iteration.

We propose using the Maxwell iteration to derive the hydrodynamic equations from the lattice Boltzmann equation (LBE) with an external forcing term. The proposed methodology differs from existing approaches in several aspects. First, it need not explicitly introduce multiple-timescales or the Knudsen number, both of which are required in the Chapman-Enskog analysis. Second, it need not use the Hilbert expansion of the hydrodynamic variables, which is necessary in the asymptotic analysis of the LBE. The proposed methodology assumes the acoustic scaling (or the convective scaling) δ(t)∼δ(x), thus δ(t) is the only expansion parameter in the analysis of the LBE system, and it leads to the Navier-Stokes equations in compressible form. The forcing density derived in this work can reproduce existing forcing schemes by adjusting appropriate parameters. The proposed methodology also analyzes the numerical accuracy of the LBE. In particular, it shows the Mach number Ma should scale as O(δ(t)(1/3)) to maintain the truncation errors due to Ma and δ(t) in balance when δ(t)→0, so that the LBE can converge to the expected hydrodynamic equations effectively and efficiently.

Reply to "Comment on 'Numerics of the lattice Boltzmann method: Effects of collision models on the lattice Boltzmann simulations'".

This Reply addresses two issues raised in the Comment [Phys. Rev. E 84, 068701 (2011)] by Karlin, Succi, and Chikatamarla (KSC): (1) A lattice Boltzmann (LB) model, which is claimed to have an H theorem, is not qualified to be called an entropic lattice Boltzmann equation (ELBE); and (2) the real ELBE with a variable relaxation time performs exceedingly well, as exhibited by their simulations of decaying "Kida vortex" flow in a three-dimensional periodic cube free of no-slip boundary. The first issue is a semantic one. We note that it was Karlin, Succi, and others who "prove the H theorem for lattice Bhatnagar-Gross-Krook models," which is the model we called ELBE in our original study to distinguish it from the usual lattice BGK model without the H theorem. Regardless of how this model is named, it does not affect the results and conclusions of our study in any way. Second, the focus of our original study is to quantify the errors of various LB models near no-slip boundaries. Hence, KSC's example, which is free of no-slip boundaries, is not relevant to our study. The results in our original paper are valid and its conclusions remain unchallenged. On the other hand, KSC's assertion that their real ELBE "provides a reliable subgrid simulation" of turbulence is not substantiated.

Accuracy of the viscous stress in the lattice Boltzmann equation with simple boundary conditions.

Based on the theory of asymptotic analysis, we prove that the viscous stress tensor computed with the lattice Boltzmann equation (LBE) in a two-dimensional domain is indeed second-order accurate in space. We only consider simple bounce-back boundary conditions which can be reduced to the periodic boundary conditions by using the method of image. While the LBE with nine velocities on two-dimensional square lattice (i.e., the D2Q9 model) and with the Bhatnagar-Gross-Krook collision model is used as an example in this work, our proof can be extended to the LBE with any linear relaxation collision models in both two and three dimensions.

Comment on "Heat transfer and fluid flow in microchannels and nanochannels at high Knudsen number using thermal lattice-Boltzmann method".

In this Comment we reveal the falsehood of the claim that the lattice Bhatnagar-Gross-Krook (BGK) model "is capable of modeling shear-driven, pressure-driven, and mixed shear-pressure-driven rarified [sic] flows and heat transfer up to Kn=1 in the transitional regime" made in a recent paper [Ghazanfarian and Abbassi, Phys. Rev. E 82, 026307 (2010)]. In particular, we demonstrate that the so-called "Knudsen effects" described are merely numerical artifacts of the lattice BGK model and they are unphysical. Specifically, we show that the erroneous results for the pressure-driven flow in a microchannel imply the false and unphysical condition that 6σKn<-1, where Kn is the Knudsen number σ=(2-σ(v))/σ(v) and σ(v)∈(0,1] is the tangential momentum accommodation coefficient. We also show explicitly that the defects of the lattice BGK model can be completely removed by using the multiple-relaxation-time collision model.

Numerics of the lattice Boltzmann method: effects of collision models on the lattice Boltzmann simulations.

We conduct a comparative study to evaluate several lattice Boltzmann (LB) models for solving the near incompressible Navier-Stokes equations, including the lattice Boltzmann equation with the multiple-relaxation-time (MRT), the two-relaxation-time (TRT), the single-relaxation-time (SRT) collision models, and the entropic lattice Boltzmann equation (ELBE). The lid-driven square cavity flow in two dimensions is used as a benchmark test. Our results demonstrate that the ELBE does not improve the numerical stability of the SRT or the lattice Bhatnagar-Gross-Krook (LBGK) model. Our results also show that the MRT and TRT LB models are superior to the ELBE and LBGK models in terms of accuracy, stability, and computational efficiency and that the ELBE scheme is the most inferior among the LB models tested in this study, thus is unfit for carrying out numerical simulations in practice. Our study suggests that, to optimize the accuracy, stability, and efficiency in the MRT model, it requires at least three independently adjustable relaxation rates: one for the shear viscosity ν (or the Reynolds number Re), one for the bulk viscosity ζ, and one to satisfy the criterion imposed by the Dirichlet boundary conditions which are realized by the bounce-back-type boundary conditions.

Effects of multitemperature nonequilibrium on compressible homogeneous turbulence.

We study the effects of the rotational-translational energy exchange on the compressible decaying homogeneous isotropic turbulence (DHIT) in three dimensions through direct numerical simulations. We use the gas-kinetic scheme coupled with multitemperature nonequilibrium based on the Jeans-Landau-Teller model. We investigate the effects of the relaxation time of rotational temperature, ZR, and the initial ratio of the rotational and translational temperatures, TR0/TL0, on the dynamics of various turbulence statistics including the kinetic energy K(t), the dissipation rate epsilon(t), the energy spectrum E(k,t), the root mean square of the velocity divergence theta'(t), the skewness Su(t) and the flatness Fu(t) of the velocity derivatives, and the probability distribution functions of the local Mach number Ma and the shocklet strength chi. The larger the ZR is, the faster the compressibility decays after an initial time. Similarly, with a fixed TL0, the higher the initial energy ratio TR0/TL0, the weaker is the compressibility in the flow. It is also observed that the effect of TR0/TL0 is strong in all times in the decay, while the effect of ZR is severe only in the later times passing through the stage with strong nonlinearity. We also observe that the multitemperature model does not affect the self-similarities obeyed by the probability distribution functions of Ma and chi , which appear to be a robust feature of the compressible DHIT.

Gas-kinetic schemes for direct numerical simulations of compressible homogeneous turbulence.

We apply the gas-kinetic scheme (GKS) for the direct numerical simulations (DNSs) of compressible decaying homogeneous isotropic turbulence (DHIT). We intend to study the accuracy, stability, and efficiency of the gas-kinetic scheme for DNS of compressible homogeneous turbulence depending on both flow conditions and numerics. In particular, we study the GKS with multidimensional, quasi-one-dimensional, dimensional-splitting, and smooth-flow approximations. We simulate the compressible DHIT with the Taylor microscale Reynolds number Re(lambda)=72.0 and the turbulence Mach number Ma(t) between 0.1 and 0.6. We compute the low-order statistical quantities including the total kinetic energy K(t), the dissipation rate epsilon(t), the skewness S(u)(t), and the flatness F(u)(t) of the velocity field u(x,t). We assess the effects on the turbulence statistics due to the approximations made in the treatment of fluxes, the flux limiter, the accuracy of the interpolation, and the bulk viscosity. Our results show that the GKS is adequate for DNS of compressible homogeneous turbulence as far as the low-order turbulence statistics are concerned.

Theory of the lattice Boltzmann equation: symmetry properties of discrete velocity sets.

The lattice Boltzmann equation replaces continuous particle velocity space by a finite set; the velocity distribution function then varies over a finite-dimensional vector space instead of over an infinite-dimensional function space. The number of linearly independent moments of the distribution function in a lattice Boltzmann model cannot exceed the number of velocities; finite dimensionality therefore necessarily induces linear dependences among the moments that do not exist in a continuous theory. Given a finite velocity set, it is important to know which moments are free of these dependences. Elementary group theory is applied to the solution of this problem. It is found that decomposing the velocity set into subsets that transform among themselves under an appropriate symmetry group makes it straightforward to uncover linear dependences among the moments. The construction of some standard two- and three-dimensional models is reviewed from this viewpoint, and procedures for constructing higher-dimensional models are suggested.

Comment on "Alternative approach to the solution of the dispersion relation for a generalized lattice Boltzmann equation".

Recently Reis and Phillips [Phys. Rev. E 77, 026702 (2008)] proposed a perturbative method to solve the dispersion equation derived from the linearized lattice Boltzmann equation. We will demonstrate that the method proposed by Reis and Phillips is a reinvention of an existing method. We would also like to refute a number of claims made by Reis and Phillips.

Lattice Boltzmann simulations of decaying homogeneous isotropic turbulence.

Decaying homogeneous isotropic turbulence in inertial and rotating reference frames is investigated to evaluate the capability of the lattice Boltzmann method in turbulence. In the inertial frame case, the decay exponents of kinetic energy and dissipation and the low wave-number scaling of the spectrum are studied. The results are in agreement with classical ones. In the frame-rotation case, simulations show that the energy decay rate decreases with decreasing Rossby number as the energy cascade is inhibited by rotation, again in agreement with turbulence physics. These results clearly indicate that the lattice Boltzmann method captures important features of decaying turbulence.

Theory of the lattice Boltzmann method: acoustic and thermal properties in two and three dimensions.

The focus of the present work is to provide an analysis for the acoustic and thermal properties of the energy-conserving lattice Boltzmann models, and a solution to the numerical defects and instability associated with these models in two and three dimensions. We discover that a spurious algebraic coupling between the shear and energy modes of the linearized evolution operator is a defect universal to the energy-conserving Boltzmann models in two and three dimensions. This spurious mode coupling is highly anisotropic and may occur at small values of wave number k along certain directions, and it is a direct consequence of the following key features of the lattice Boltzmann equation: (1) its simple spatial-temporal dynamics, (2) the linearity of the relaxation modeling for collision operator, and (3) the energy-conservation constraint. To eliminate the spurious mode coupling, we propose a hybrid thermal lattice Boltzmann equation (HTLBE) in which the mass and momentum conservation equations are solved by using the multiple-relaxation-time model due to d'Humières, whereas the diffusion-advection equation for the temperature is solved separately by using finite-difference technique (or other means). Through the Chapman-Enskog analysis we show that the hydrodynamic equations derived from the proposed HTLBE model include the equivalent effect of gamma=C(P)/C(V) in both the speed and attenuation of sound. Appropriate coupling between the energy and velocity field is introduced to attain correct acoustics in the model. The numerical stability of the HTLBE scheme is analyzed by solving the dispersion equation of the linearized collision operator. We find that the numerical stability of the lattice Boltzmann scheme improves drastically once the spurious mode coupling is removed. It is shown that the HTLBE scheme is far superior to the existing thermal LBE schemes in terms of numerical stability, flexibility, and possible generalization for complex fluids. We also present the simulation results of the convective flow in a rectangular cavity with different temperatures on two opposite vertical walls and under the influence of gravity. Our numerical results agree well with the pseudospectral result.

Nonexistence of H theorems for the athermal lattice Boltzmann models with polynomial equilibria.

We prove that no H theorem exists for the athermal lattice Boltzmann equation with polynomial equilibria satisfying the conservation laws exactly and explicitly. The proof is demonstrated by using the seven-velocity model in a triangular lattice in two dimensions, and can be readily extended to other lattice Boltzmann models in two and three dimensions. Some issues pertinent to the numerical instabilities of the lattice Boltzmann method are discussed.

Theory of the lattice Boltzmann method: two-fluid model for binary mixtures.

A two-fluid lattice Boltzmann model for binary mixtures is developed. The model is derived formally from kinetic theory by discretizing two-fluid Boltzmann equations in which mutual collisions and self-collisions are treated independently. In the resulting lattice Boltzmann model, viscosity and diffusion coefficients can be varied independently by a suitable choice of mutual- and self-collision relaxation-time scales. Further, the proposed model can simulate miscible and immiscible fluids by changing the sign of the mutual-collision term. This is in contrast to most existing single-fluid lattice Boltzmann models that employ a single-relaxation-time scale and hence are restricted to unity Prandtl and Schmidt numbers. The extension of binary mixing model to multiscalar mixing is quite straightforward.

Theory of the lattice Boltzmann method: three-dimensional model for linear viscoelastic fluids.

A three-dimensional lattice Boltzmann model with thirty two discrete velocity distribution functions for viscoelastic fluid is presented in this work. The model is based upon the generalized lattice Boltzmann equation constructed in moment space. The nonlinear equilibria of the model have a number of coupling constants that are free parameters. The dispersion equation of the model is analyzed under various conditions to obtain the constraints on the free parameters such that the model satisfies isotropy and Galilean invariance. The macroscopic equations are also derived from the lattice Boltzmann model through the dispersion equation analysis and the Chapman-Enskog analysis. We demonstrate that the dispersion equation analysis can be used as a general and effective means to derive hydrodynamic equations, excluding some nonlinear source terms, from the lattice Boltzmann model, to obtain conditions for its isotropy and Galilean invariance, and to optimize its stability. We show that the hydrodynamic behavior of the lattice Boltzmann model has memory effects, and that in the linear regime, it behaves as a viscoelastic fluid described by the Jeffreys model. Some numerical results to verify the theoretical analysis of the model are also presented.

Lattice Boltzmann model for binary mixtures.

An a priori derivation of the lattice Boltzmann equations for binary mixtures is provided by discretizing the Boltzmann equations that govern the evolution of binary mixtures. The present model leads to a set of two-fluid hydrodynamic equations for the mixture. In existing models, employing the single-relaxation-time approximation, the viscosity and diffusion coefficients are coupled through the relaxation parameter tau, thus limited to unity Prandtl number and Schmidt number. In the present model the viscosity and diffusion coefficient are independently controlled by two relaxation parameters, thus enabling the modeling of mixtures with an arbitrary Schmidt number. The theoretical framework developed here can be readily applied to multiple-species mixing.

Force evaluation in the lattice Boltzmann method involving curved geometry.

The present work investigates two approaches for force evaluation in the lattice Boltzmann equation: the momentum-exchange method and the stress-integration method on the surface of a body. The boundary condition for the particle distribution functions on curved geometries is handled with second-order accuracy based on our recent works [Mei et al., J. Comput. Phys. 155, 307 (1999); ibid. 161, 680 (2000)]. The stress-integration method is computationally laborious for two-dimensional flows and in general difficult to implement for three-dimensional flows, while the momentum-exchange method is reliable, accurate, and easy to implement for both two-dimensional and three-dimensional flows. Several test cases are selected to evaluate the present methods, including: (i) two-dimensional pressure-driven channel flow; (ii) two-dimensional uniform flow past a column of cylinders; (iii) two-dimensional flow past a cylinder asymmetrically placed in a channel (with vortex shedding); (iv) three-dimensional pressure-driven flow in a circular pipe; and (v) three-dimensional flow past a sphere. The drag evaluated by using the momentum-exchange method agrees well with the exact or other published results.

Multiple-relaxation-time lattice Boltzmann models in three dimensions.

This article provides a concise exposition of the multiple-relaxation-time lattice Boltzmann equation, with examples of 15-velocity and 19-velocity models in three dimensions. Simulation of a diagonally lid-driven cavity flow in three dimensions at Re = 500 and 2000 is performed. The results clearly demonstrate the superior numerical stability of the multiple-relaxation-time lattice Boltzmann equation over the popular lattice Bhatnagar-Gross-Krook equation.