BACKGROUND Most trauma occurs among young male subjects in Qatar.We examined the predictive values of the delta shock index(DSI),defined as the change in the shock index(SI)value from the scene to the initial reading ...BACKGROUND Most trauma occurs among young male subjects in Qatar.We examined the predictive values of the delta shock index(DSI),defined as the change in the shock index(SI)value from the scene to the initial reading in the emergency unit(i.e.,subtracting the calculated SI at admission from SI at the scene),at a Level 1 trauma center.AIM To explore whether high DSI is associated with severe injuries,more interventions,and worse outcomes[i.e.,blood transfusion,exploratory laparotomy,ventilator-associated pneumonia,hospital length of stay(HLOS),and in-hospital mortality]in trauma patients.METHODS A retrospective analysis was conducted after data were extracted from the National Trauma Registry between 2011 and 2021.Patients were grouped based on DSI as low(≤0.1)or high(>0.1).Data were analyzed and compared usingχ2 and Student’s t-tests.Correlations between DSI and injury severity score(ISS),revised trauma score(RTS),abbreviated injury scale(AIS),Glasgow coma scale(GCS),trauma score-ISS(TRISS),HLOS,and number of transfused blood units(NTBU),were assessed using correlation coefficient analysis.The diagnostic testing accuracy for predicting mortality was determined using the validity measures of the DSI.Logistic regression analysis was performed to identify predictors of mortality.RESULTS This analysis included 13212 patients with a mean age of 33±14 years,and 24%had a high DSI.Males accounted for 91%of the study population.The trauma activation level was higher in patients with a high DSI(38%vs 15%,P=0.001).DSI correlated with RTS(r=-0.30),TRISS(r=-0.30),NTBU(r=0.20),GCS(r=-0.24),ISS(r=0.22),and HLOS(r=0.14)(P=0.001 for all).High DSI was associated with significantly higher rates of intubation,laparotomy,ventilator-associated pneumonia,massive transfusion activation,and mortality than low DSI.For mortality prediction,a high DSI had better specificity,negative predictive value,and negative likelihood ratio(77%,99%,and 0.49%,respectively).After adjusting for age,emergency medical services time,GCS score,and ISS,multivariable regression analysis showed that DSI was an independent predictor of mortality(odds ratio=1.9;95%confidence interval:1.35-2.76).CONCLUSION In addition to sex-biased observations,almost one-quarter of the study cohort had a higher DSI and were mostly young.High DSI correlated significantly with the other injury severity scores,which require more time and imaging to be ready to use.Therefore,DSI is a practical,simple bedside tool for triaging and prognosis in young patients with trauma.展开更多
The Riemann problems for the Euler system of conservation laws of energy and momentum in special relativity as pressure vanishes are considered. The Riemann solutions for the pressureless relativistic Euler equations ...The Riemann problems for the Euler system of conservation laws of energy and momentum in special relativity as pressure vanishes are considered. The Riemann solutions for the pressureless relativistic Euler equations are obtained constructively. There are two kinds of solutions, the one involves delta shock wave and the other involves vacuum. The authors prove that these two kinds of solutions are the limits of the solutions as pressure vanishes in the Euler system of conservation laws of energy and momentum in special relativity.展开更多
For a nonlinear hyperbolic system of conservation laws, the initial-boundary value problem is concerned with the boundary conditions. A boundary entropy condition is derived based on Dubois F and Le Floch P＇s results...For a nonlinear hyperbolic system of conservation laws, the initial-boundary value problem is concerned with the boundary conditions. A boundary entropy condition is derived based on Dubois F and Le Floch P＇s results by taking a suitable entropy-flux pair （Journal of Differential Equations, 1988, 71（1）： 93-122）. The solutions of the initial-boundary value problem for the system are constructively obtained, in which initial-boundary data are in piecewise constant states. The delta-shock waves appear in their solutions.展开更多
We consider the singular Riemann problem for the rectilinear isentropic compressible Euler equations with discontinuous flux,more specifically,for pressureless flow on the left and polytropic flow on the right separat...We consider the singular Riemann problem for the rectilinear isentropic compressible Euler equations with discontinuous flux,more specifically,for pressureless flow on the left and polytropic flow on the right separated by a discontinuity x=x(t).We prove that this problem admits global Radon measure solutions for all kinds of initial data.The over-compressing condition on the discontinuity x=x(t)is not enough to ensure the uniqueness of the solution.However,there is a unique piecewise smooth solution if one proposes a slip condition on the right-side of the curve x=x(t)+0,in addition to the full adhesion condition on its left-side.As an application,we study a free piston problem with the piston in a tube surrounded initially by uniform pressureless flow and a polytropic gas.In particular,we obtain the existence of a piecewise smooth solution for the motion of the piston between a vacuum and a polytropic gas.This indicates that the singular Riemann problem looks like a control problem in the sense that one could adjust the condition on the discontinuity of the flux to obtain the desired flow field.展开更多
In this article, we study the Riemann problem with delta initial data for the one-dimensional Chaplygin gas equations. Under the generalized Rankine-Hugoniot conditions and the entropy condition, we constructively obt...In this article, we study the Riemann problem with delta initial data for the one-dimensional Chaplygin gas equations. Under the generalized Rankine-Hugoniot conditions and the entropy condition, we constructively obtain the global existence of generalized solutions that explicitly exhibit four kinds of different structures. Moreover, we obtain the stability of generalized solutions by making use of the perturbation of the initial data.展开更多
We solve the Riemann problems for isentropic compressible Euler equations of polytropic gases in the class of Radon measures,and the solutions admit the concentration of mass.It is found that under the requirement of ...We solve the Riemann problems for isentropic compressible Euler equations of polytropic gases in the class of Radon measures,and the solutions admit the concentration of mass.It is found that under the requirement of satisfying the over-compressing entropy condition:(i)there is a unique delta shock solution,corresponding to the case that has two strong classical Lax shocks;(ii)for the initial data that the classical Riemann solution contains a shock wave and a rarefaction wave,or two shocks with one being weak,there are infinitely many solutions,each consists of a delta shock and a rarefaction wave;(iii)there are no delta shocks for the case that the classical entropy weak solutions consist only of rarefaction waves.These solutions are self-similar.Furthermore,for the generalized Riemann problem with mass concentrated initially at the discontinuous point of initial data,there always exists a unique delta shock for at least a short time.It could be prolonged to a global solution.Not all the solutions are self-similar due to the initial velocity of the concentrated point-mass(particle).Whether the delta shock solutions constructed satisfy the over-compressing entropy condition is clarified.This is the first result on the construction of singular measure solutions to the compressible Euler system of polytropic gases,that is strictly hyperbolic,and whose characteristics are both genuinely nonlinear.We also discuss possible physical interpretations and applications of these new solutions.展开更多
研究了带有Chaplygin压力的耦合Aw-Rascle(CAR)交通模型的黎曼问题.通过令耦合模型两侧压力同时消失,得到上述黎曼解的极限,并证明了该极限具有相同初值的无压气体动力(Pressureless Gas Dynamics,PGD)模型的黎曼解.更进一步,证得极限后...研究了带有Chaplygin压力的耦合Aw-Rascle(CAR)交通模型的黎曼问题.通过令耦合模型两侧压力同时消失,得到上述黎曼解的极限,并证明了该极限具有相同初值的无压气体动力(Pressureless Gas Dynamics,PGD)模型的黎曼解.更进一步,证得极限后的delta激波解的权重和速度与PGD模型的delta激波解的权重和速度完全一致.此外,由解的渐近行为,可以观察到稀疏接触间断到接触间断的转化.展开更多
In this paper,firstly,by solving the Riemann problem of the zero-pressure flow in gas dynamics with a flux approximation,we construct parameterized delta-shock and constant density solutions,then we show that,as the f...In this paper,firstly,by solving the Riemann problem of the zero-pressure flow in gas dynamics with a flux approximation,we construct parameterized delta-shock and constant density solutions,then we show that,as the flux perturbation vanishes,they converge to the delta-shock and vacuum state solutions of the zero-pressure flow,respectively.Secondly,we solve the Riemann problem of the Euler equations of isentropic gas dynamics with a double parameter flux approximation including pressure.Furthermore,we rigorously prove that,as the two-parameter flux perturbation vanishes,any Riemann solution containing two shock waves tends to a delta-shock solution to the zero-pressure flow;any Riemann solution containing two rarefaction waves tends to a two-contact-discontinuity solution to the zero-pressure flow and the nonvacuum intermediate state in between tends to a vacuum state.Finally,numerical results are given to present the formation processes of delta shock waves and vacuum states.展开更多
In this paper, we investigate the elementary wave interactions of the Aw-Rascle model for the generalized Chaplygin gas. We construct the unique solution by the characteristic analysis method and obtain the stability ...In this paper, we investigate the elementary wave interactions of the Aw-Rascle model for the generalized Chaplygin gas. We construct the unique solution by the characteristic analysis method and obtain the stability of the corresponding Riemann solutions under such small perturbations on the initial values. We find that the elementary wave interactions have a much more simple structure for Temple class than general systems of conservation laws. It is important to study the elementary waves interactions of the traffic flow system for the generalized Chaplygin gas not only because of their significance in practical applications in the traffic flow system, but also because of their basic role for the general mathematical theory.展开更多
基金The Medical Research Center(institutional review board,MRC-01-21-990)approved the study protocol at Hamad Medical Corporation,Doha,Qatar.
文摘BACKGROUND Most trauma occurs among young male subjects in Qatar.We examined the predictive values of the delta shock index(DSI),defined as the change in the shock index(SI)value from the scene to the initial reading in the emergency unit(i.e.,subtracting the calculated SI at admission from SI at the scene),at a Level 1 trauma center.AIM To explore whether high DSI is associated with severe injuries,more interventions,and worse outcomes[i.e.,blood transfusion,exploratory laparotomy,ventilator-associated pneumonia,hospital length of stay(HLOS),and in-hospital mortality]in trauma patients.METHODS A retrospective analysis was conducted after data were extracted from the National Trauma Registry between 2011 and 2021.Patients were grouped based on DSI as low(≤0.1)or high(>0.1).Data were analyzed and compared usingχ2 and Student’s t-tests.Correlations between DSI and injury severity score(ISS),revised trauma score(RTS),abbreviated injury scale(AIS),Glasgow coma scale(GCS),trauma score-ISS(TRISS),HLOS,and number of transfused blood units(NTBU),were assessed using correlation coefficient analysis.The diagnostic testing accuracy for predicting mortality was determined using the validity measures of the DSI.Logistic regression analysis was performed to identify predictors of mortality.RESULTS This analysis included 13212 patients with a mean age of 33±14 years,and 24%had a high DSI.Males accounted for 91%of the study population.The trauma activation level was higher in patients with a high DSI(38%vs 15%,P=0.001).DSI correlated with RTS(r=-0.30),TRISS(r=-0.30),NTBU(r=0.20),GCS(r=-0.24),ISS(r=0.22),and HLOS(r=0.14)(P=0.001 for all).High DSI was associated with significantly higher rates of intubation,laparotomy,ventilator-associated pneumonia,massive transfusion activation,and mortality than low DSI.For mortality prediction,a high DSI had better specificity,negative predictive value,and negative likelihood ratio(77%,99%,and 0.49%,respectively).After adjusting for age,emergency medical services time,GCS score,and ISS,multivariable regression analysis showed that DSI was an independent predictor of mortality(odds ratio=1.9;95%confidence interval:1.35-2.76).CONCLUSION In addition to sex-biased observations,almost one-quarter of the study cohort had a higher DSI and were mostly young.High DSI correlated significantly with the other injury severity scores,which require more time and imaging to be ready to use.Therefore,DSI is a practical,simple bedside tool for triaging and prognosis in young patients with trauma.
基金supported by the National Natural Science Foundation of China (No. 10671120)the ShanghaiLeading Academic Discipline Project (No. J50101).
文摘The Riemann problems for the Euler system of conservation laws of energy and momentum in special relativity as pressure vanishes are considered. The Riemann solutions for the pressureless relativistic Euler equations are obtained constructively. There are two kinds of solutions, the one involves delta shock wave and the other involves vacuum. The authors prove that these two kinds of solutions are the limits of the solutions as pressure vanishes in the Euler system of conservation laws of energy and momentum in special relativity.
基金Project supported by the National Natural Science Foundation of China （Grant No.10671120）
文摘For a nonlinear hyperbolic system of conservation laws, the initial-boundary value problem is concerned with the boundary conditions. A boundary entropy condition is derived based on Dubois F and Le Floch P＇s results by taking a suitable entropy-flux pair （Journal of Differential Equations, 1988, 71（1）： 93-122）. The solutions of the initial-boundary value problem for the system are constructively obtained, in which initial-boundary data are in piecewise constant states. The delta-shock waves appear in their solutions.
基金supported by the National Natural Science Foundation of China(11871218,12071298)in part by the Science and Technology Commission of Shanghai Municipality(21JC1402500,22DZ2229014)。
文摘We consider the singular Riemann problem for the rectilinear isentropic compressible Euler equations with discontinuous flux,more specifically,for pressureless flow on the left and polytropic flow on the right separated by a discontinuity x=x(t).We prove that this problem admits global Radon measure solutions for all kinds of initial data.The over-compressing condition on the discontinuity x=x(t)is not enough to ensure the uniqueness of the solution.However,there is a unique piecewise smooth solution if one proposes a slip condition on the right-side of the curve x=x(t)+0,in addition to the full adhesion condition on its left-side.As an application,we study a free piston problem with the piston in a tube surrounded initially by uniform pressureless flow and a polytropic gas.In particular,we obtain the existence of a piecewise smooth solution for the motion of the piston between a vacuum and a polytropic gas.This indicates that the singular Riemann problem looks like a control problem in the sense that one could adjust the condition on the discontinuity of the flux to obtain the desired flow field.
基金supported by National Natural Science Foundation of China (10871199)
文摘In this article, we study the Riemann problem with delta initial data for the one-dimensional Chaplygin gas equations. Under the generalized Rankine-Hugoniot conditions and the entropy condition, we constructively obtain the global existence of generalized solutions that explicitly exhibit four kinds of different structures. Moreover, we obtain the stability of generalized solutions by making use of the perturbation of the initial data.
基金supported by the National Natural Science Foundation of China under Grants No.11871218,No.12071298the Science and Technology Commission of Shanghai Municipality under Grant No.18dz2271000.
文摘We solve the Riemann problems for isentropic compressible Euler equations of polytropic gases in the class of Radon measures,and the solutions admit the concentration of mass.It is found that under the requirement of satisfying the over-compressing entropy condition:(i)there is a unique delta shock solution,corresponding to the case that has two strong classical Lax shocks;(ii)for the initial data that the classical Riemann solution contains a shock wave and a rarefaction wave,or two shocks with one being weak,there are infinitely many solutions,each consists of a delta shock and a rarefaction wave;(iii)there are no delta shocks for the case that the classical entropy weak solutions consist only of rarefaction waves.These solutions are self-similar.Furthermore,for the generalized Riemann problem with mass concentrated initially at the discontinuous point of initial data,there always exists a unique delta shock for at least a short time.It could be prolonged to a global solution.Not all the solutions are self-similar due to the initial velocity of the concentrated point-mass(particle).Whether the delta shock solutions constructed satisfy the over-compressing entropy condition is clarified.This is the first result on the construction of singular measure solutions to the compressible Euler system of polytropic gases,that is strictly hyperbolic,and whose characteristics are both genuinely nonlinear.We also discuss possible physical interpretations and applications of these new solutions.
文摘研究了带有Chaplygin压力的耦合Aw-Rascle(CAR)交通模型的黎曼问题.通过令耦合模型两侧压力同时消失,得到上述黎曼解的极限,并证明了该极限具有相同初值的无压气体动力(Pressureless Gas Dynamics,PGD)模型的黎曼解.更进一步,证得极限后的delta激波解的权重和速度与PGD模型的delta激波解的权重和速度完全一致.此外,由解的渐近行为,可以观察到稀疏接触间断到接触间断的转化.
基金supported by National Natural Science Foundation of China(Grant No.11361073)
文摘In this paper,firstly,by solving the Riemann problem of the zero-pressure flow in gas dynamics with a flux approximation,we construct parameterized delta-shock and constant density solutions,then we show that,as the flux perturbation vanishes,they converge to the delta-shock and vacuum state solutions of the zero-pressure flow,respectively.Secondly,we solve the Riemann problem of the Euler equations of isentropic gas dynamics with a double parameter flux approximation including pressure.Furthermore,we rigorously prove that,as the two-parameter flux perturbation vanishes,any Riemann solution containing two shock waves tends to a delta-shock solution to the zero-pressure flow;any Riemann solution containing two rarefaction waves tends to a two-contact-discontinuity solution to the zero-pressure flow and the nonvacuum intermediate state in between tends to a vacuum state.Finally,numerical results are given to present the formation processes of delta shock waves and vacuum states.
基金Supported by the Scientific Research Program of the Higher Education Institution of Xinjiang(XJEDU2011S02)the Ph.D Graduate Start Research Foundation of Xinjiang University Funded Project(No.BS100105 and BS090107)the National Natural Science Foundation of China(11101348)
文摘In this paper, we investigate the elementary wave interactions of the Aw-Rascle model for the generalized Chaplygin gas. We construct the unique solution by the characteristic analysis method and obtain the stability of the corresponding Riemann solutions under such small perturbations on the initial values. We find that the elementary wave interactions have a much more simple structure for Temple class than general systems of conservation laws. It is important to study the elementary waves interactions of the traffic flow system for the generalized Chaplygin gas not only because of their significance in practical applications in the traffic flow system, but also because of their basic role for the general mathematical theory.
基金Project supported by the National Natural Science Foundation of China(11371240,11771274)the Shanghai Municipal Education Commission of Scientific Research Innovation Project(11ZZ84)
