Shock wave caused by a sudden release of high-energy,such as explosion and blast,usually affects a significant range of areas.The utilization of a uniform fine mesh to capture sharp shock wave and to obtain precise re...Shock wave caused by a sudden release of high-energy,such as explosion and blast,usually affects a significant range of areas.The utilization of a uniform fine mesh to capture sharp shock wave and to obtain precise results is inefficient in terms of computational resource.This is particularly evident when large-scale fluid field simulations are conducted with significant differences in computational domain size.In this work,a variable-domain-size adaptive mesh enlargement(vAME)method is developed based on the proposed adaptive mesh enlargement(AME)method for modeling multi-explosives explosion problems.The vAME method reduces the division of numerous empty areas or unnecessary computational domains by adaptively suspending enlargement operation in one or two directions,rather than in all directions as in AME method.A series of numerical tests via AME and vAME with varying nonintegral enlargement ratios and different mesh numbers are simulated to verify the efficiency and order of accuracy.An estimate of speedup ratio is analyzed for further efficiency comparison.Several large-scale near-ground explosion experiments with single/multiple explosives are performed to analyze the shock wave superposition formed by the incident wave,reflected wave,and Mach wave.Additionally,the vAME method is employed to validate the accuracy,as well as to investigate the performance of the fluid field and shock wave propagation,considering explosive quantities ranging from 1 to 5 while maintaining a constant total mass.The results show a satisfactory correlation between the overpressure versus time curves for experiments and numerical simulations.The vAME method yields a competitive efficiency,increasing the computational speed to 3.0 and approximately 120,000 times in comparison to AME and the fully fine mesh method,respectively.It indicates that the vAME method reduces the computational cost with minimal impact on the results for such large-scale high-energy release problems with significant differences in computational domain size.展开更多
The microstructures and thermodynamic properties of mixed systems comprising pyridinium ionic liquid[HPy][BF_(4)]and acetonitrile at different mole fractions were studied using molecular dynamics simulation in this wo...The microstructures and thermodynamic properties of mixed systems comprising pyridinium ionic liquid[HPy][BF_(4)]and acetonitrile at different mole fractions were studied using molecular dynamics simulation in this work.The following properties were determined:density,self-diffusion coefficient,excess molar volume,and radial distribution function.The results show that with an increase in the mole fraction of[HPy][BF_(4)],the self-diffusion coefficient decreases.Additionally,the excess molar volume initially decreases,reaches a minimum,and then increases.The rules of radial distribution functions(RDFs)of characteristic atoms are different.With increasing the mole fraction of[HPy][BF_(4)],the first peak of the RDFs of HA1-F decreases,while that of CT6-CT6 rises at first and then decreases.This indicates that the solvent molecules affect the polar and non-polar regions of[HPy][BF_(4)]differently.展开更多
Simulation of a class of delay stochastic system with distributed parameter is discussed. Difference schemes for the numerical computation of delay stochastic system are obtained. The precision of the difference schem...Simulation of a class of delay stochastic system with distributed parameter is discussed. Difference schemes for the numerical computation of delay stochastic system are obtained. The precision of the difference scheme and the efficiency of the difference scheme in simulation of delay stochastic system with distributed parameter are analyzed. Examples are given to illustrate the application of the method.展开更多
The improved weighted-least-square model was used for state simulation of water distribution networks. And DFP algorithm was applied to get the model solution. In order to fit DFP algorithm,the initial model was trans...The improved weighted-least-square model was used for state simulation of water distribution networks. And DFP algorithm was applied to get the model solution. In order to fit DFP algorithm,the initial model was transformed into a non-constrained optimization problem using mass conservation. Then,through one dimensional optimization and scale matrix establishment,the feasible direction of iteration was obtained,and the values of state variables could be calculated. After several iterations,the optimal estimates of state variables were worked out and state simulation of water distribution networks was achieved as a result. A program of DFP algorithm is developed with Delphi 7 for verification. By running on a designed network,which is composed of 55 nodes,94 pipes and 40 loops,it is proved that DFP algorithm can quickly get the convergence. After 36 iterations,the root mean square of all nodal head errors is reduced by 90.84% from 5.57 to 0.51 m,and the maximum error is only 1.30 m. Compared to Marquardt algorithm,the procedure of DFP algorithm is more stable,and the initial values have less influences on calculation accuracy. Therefore,DFP algorithm can be used for real-time simulation of water distribution networks.展开更多
Decentralized robust stabilization problem of discrete-time fuzzy large-scale systems with parametric uncertainties is considered. This uncertain fuzzy large-scale system consists of N interconnected T-S fuzzy subsyst...Decentralized robust stabilization problem of discrete-time fuzzy large-scale systems with parametric uncertainties is considered. This uncertain fuzzy large-scale system consists of N interconnected T-S fuzzy subsystems, and the parametric uncertainties are unknown but norm-bounded. Based on Lyapunov stability theory and decentralized control theory of large-scale system, the design schema of decentralized parallel distributed compensation （DPDC） fuzzy controllers to ensure the asymptotic stability of the whole fuzzy large-scale system is proposed. The existence conditions for these controllers take the forms of LMIs. Finally a numerical simulation example is given to show the utility of the method proposed.展开更多
An integrated simulation system for solar sail spacecraft with individually controllable elements(SSICE)is investigated in this paper,including the modelling of power management,thermal control,attitude control,umbra ...An integrated simulation system for solar sail spacecraft with individually controllable elements(SSICE)is investigated in this paper,including the modelling of power management,thermal control,attitude control,umbra prediction,and orbit prediction subsystems.Considering the self-control and reactivity subsystems,an agent based method is applied to develop the subsystem models.Each subsystem is an individual agent component,which manages itself autonomously and reacts to the requirements from other agents.To reduce computing burden on a specified computer and improve the suitability and flexibility of the integrated simulation system,a distributed framework is employed in the system by deploying agent components on different computers.The data transmission among agents is based on the transmission control protocol/Internet protocol(TCP/IP).A practical example of sun pointing is used to test the operating effect of the integrated system and the working condition of subsystems.The simulation results verify that the integrated system has higher sun pointing accuracy,quicker dynamical response to variations of the lighting,attitude and temperature and fewer computing resources with effective and accurate subsystems.The integrated system proposed in this paper can be applied to solar sail design,operation,and mission planning.展开更多
Considering the fact that the temperature distribution in furnace of a tangential fired pulverized coal boiler is difficult to be measured and monitored, two-stage numerical simulation method was put forward. First, m...Considering the fact that the temperature distribution in furnace of a tangential fired pulverized coal boiler is difficult to be measured and monitored, two-stage numerical simulation method was put forward. First, multi-field coupling simulation in typical work conditions was carried out off-line with the software CFX-4.3, and then the expression of temperature profile varying with operating parameter was obtained. According to real-time operating parameters, the temperature at arbitrary point of the furnace can be calculated by using this expression. Thus the temperature profile can be shown on-line and monitoring for combustion state in the furnace is realized. The simul-(ation) model was checked by the parameters measured in an operating boiler, (DG130-9.8/540.) The maximum of relative error is less than 12% and the absolute error is less than 120℃, which shows that the proposed two-stage simulation method is reliable and able to satisfy the requirement of industrial application.展开更多
Multiple earth observing satellites need to communicate with each other to observe plenty of targets on the Earth together. The factors, such as external interference, result in satellite information interaction delay...Multiple earth observing satellites need to communicate with each other to observe plenty of targets on the Earth together. The factors, such as external interference, result in satellite information interaction delays, which is unable to ensure the integrity and timeliness of the information on decision making for satellites. And the optimization of the planning result is affected. Therefore, the effect of communication delay is considered during the multi-satel ite coordinating process. For this problem, firstly, a distributed cooperative optimization problem for multiple satellites in the delayed communication environment is formulized. Secondly, based on both the analysis of the temporal sequence of tasks in a single satellite and the dynamically decoupled characteristics of the multi-satellite system, the environment information of multi-satellite distributed cooperative optimization is constructed on the basis of the directed acyclic graph（DAG）. Then, both a cooperative optimization decision making framework and a model are built according to the decentralized partial observable Markov decision process（DEC-POMDP）. After that, a satellite coordinating strategy aimed at different conditions of communication delay is mainly analyzed, and a unified processing strategy on communication delay is designed. An approximate cooperative optimization algorithm based on simulated annealing is proposed. Finally, the effectiveness and robustness of the method presented in this paper are verified via the simulation.展开更多
Numerical simulations of gas–liquid two-phase flow and alumina transport process in an aluminum reduction cell were conducted to investigate the effects of anode configurations on the bath flow, gas volume fraction a...Numerical simulations of gas–liquid two-phase flow and alumina transport process in an aluminum reduction cell were conducted to investigate the effects of anode configurations on the bath flow, gas volume fraction and alumina content distributions. An Euler–Euler two-fluid model was employed coupled with a species transport equation for alumina content. Three different anode configurations such as anode without a slot, anode with a longitudinal slot and anode with a transversal slot were studied in the simulation. The simulation results clearly show that the slots can reduce the bath velocity and promote the releasing of the anode gas, but can not contribute to the uniformity of the alumina content. Comparisons of the effects between the longitudinal and transversal slots indicate that the longitudinal slot is better in terms of gas–liquid flow but is disadvantageous for alumina mixing and transport process due to a decrease of anode gas under the anode bottom surface. It is demonstrated from the simulations that the mixing and transfer characteristics of alumina are controlled to great extent by the anode gas forces while the electromagnetic forces(EMFs) play the second role.展开更多
The study of non-axisymmetric fuel dispersal and detonation can provide reference for the prevention of industrial cloud explosion accidents and the design of fuel air explosive(FAE).The concentration and detonation f...The study of non-axisymmetric fuel dispersal and detonation can provide reference for the prevention of industrial cloud explosion accidents and the design of fuel air explosive(FAE).The concentration and detonation fields of 85 kg cylindrical and fan-shaped fuel are investigated by experiments and numerical simulations.A dynamic model of the whole process for fuel dispersal and detonation is built.The concentration distribution of fuel is used as the initial condition to calculate the detonation stage,thus solving the initial value problem of detonation field.The phase and component changes of fuel cloud at different locations are compared.The fuel cloud is divided into directions of 0°,90°,135°and 180°.The results show that the maximum cloud radius is 20.94 m in 135°and the minimum is 12.04 m in 0°.The diameter of the detonation fireball is 53.6 m,and the peak temperature is 3455 K.The highest peak overpressure is 3.44 MPa in 0°and the lowest is 2.97 MPa in 135°.The proportion of liquid phase in 0°is22.90%,and the fuel loss is 11.8% and 9% higher than that in 135°and cylindrical charge,respectively.The stable propagation distance of blast wave in 135°is 42.50% longer than 0°and 28.37% longer than cylindrical charge.展开更多
The study of the electric field around a surge arrester is useful for design procedures and diagnostic tests. The current work com- putes the electric field around a medium voltage gapless surge arrester using 2D and ...The study of the electric field around a surge arrester is useful for design procedures and diagnostic tests. The current work com- putes the electric field around a medium voltage gapless surge arrester using 2D and 3D representation of the arrester. The 2D simulation design, which is described in IEC 60099-4 Standard, cannot include the non symmetrical parts of the arrester geometry and the test arrange- ment. 3D simulation procedures have the advantage that takes into account these asymmetries, giving more accurate results for each measurement position. In order to confirm the suitability of the created models, the simulation results of the electric field, using the 2D and 3D edition of PC Opera, are compared with recorded measurements, which are obtained in laboratory using appropriate calibrated field meters.展开更多
Risk quantification in grade is critical for mine design and planning.Grade uncertainty is assessed using multiple grade realizations,from geostatistical conditional simulations,which are effective to evaluate local o...Risk quantification in grade is critical for mine design and planning.Grade uncertainty is assessed using multiple grade realizations,from geostatistical conditional simulations,which are effective to evaluate local or global uncertainty by honouring spatial correlation structures.The sequential Gaussian conditional simulation was used to assess uncertainty of grade estimates and illustrate simulated models in Sivas gold deposit,Turkey.In situ variability and risk quantification of the gold grade were assessed by probabilistic approach based on the sequential Gaussian simulations to yield a series of conditional maps characterized by equally probable spatial distribution of the gold grade for the study area.The simulation results were validated by a number of tests such as descriptive statistics,histogram,variogram and contour map reproductions.The case study demonstrates the efficiency of the method in assessing risk associated with geological and engineering variable such as the gold grade variability and distribution.The simulated models can be incorporated into exploration,exploitation and scheduling of the gold deposit.展开更多
In order to study the movement of the long-distance torpedo-like autonomous underwater vehicle(AUV)which is controlled by the dynamic positioning system(DPS),by adopting momentum theorem and the angular momentum theor...In order to study the movement of the long-distance torpedo-like autonomous underwater vehicle(AUV)which is controlled by the dynamic positioning system(DPS),by adopting momentum theorem and the angular momentum theorem,the appropriate movement math model for the long-distance torpedo-like AUV has been built and the thrust of DPS is distributed.Several representative movements of AUV are simulated,such as transferring between two random points and pointing circumrotation movement.The simulation result is analyzed.It shows that DPS including five thrusters can control the AUV movement steadily at low velocity.展开更多
基金supported by the National Natural Science Foundation of China(Grant Nos.12302435 and 12221002)。
文摘Shock wave caused by a sudden release of high-energy,such as explosion and blast,usually affects a significant range of areas.The utilization of a uniform fine mesh to capture sharp shock wave and to obtain precise results is inefficient in terms of computational resource.This is particularly evident when large-scale fluid field simulations are conducted with significant differences in computational domain size.In this work,a variable-domain-size adaptive mesh enlargement(vAME)method is developed based on the proposed adaptive mesh enlargement(AME)method for modeling multi-explosives explosion problems.The vAME method reduces the division of numerous empty areas or unnecessary computational domains by adaptively suspending enlargement operation in one or two directions,rather than in all directions as in AME method.A series of numerical tests via AME and vAME with varying nonintegral enlargement ratios and different mesh numbers are simulated to verify the efficiency and order of accuracy.An estimate of speedup ratio is analyzed for further efficiency comparison.Several large-scale near-ground explosion experiments with single/multiple explosives are performed to analyze the shock wave superposition formed by the incident wave,reflected wave,and Mach wave.Additionally,the vAME method is employed to validate the accuracy,as well as to investigate the performance of the fluid field and shock wave propagation,considering explosive quantities ranging from 1 to 5 while maintaining a constant total mass.The results show a satisfactory correlation between the overpressure versus time curves for experiments and numerical simulations.The vAME method yields a competitive efficiency,increasing the computational speed to 3.0 and approximately 120,000 times in comparison to AME and the fully fine mesh method,respectively.It indicates that the vAME method reduces the computational cost with minimal impact on the results for such large-scale high-energy release problems with significant differences in computational domain size.
文摘The microstructures and thermodynamic properties of mixed systems comprising pyridinium ionic liquid[HPy][BF_(4)]and acetonitrile at different mole fractions were studied using molecular dynamics simulation in this work.The following properties were determined:density,self-diffusion coefficient,excess molar volume,and radial distribution function.The results show that with an increase in the mole fraction of[HPy][BF_(4)],the self-diffusion coefficient decreases.Additionally,the excess molar volume initially decreases,reaches a minimum,and then increases.The rules of radial distribution functions(RDFs)of characteristic atoms are different.With increasing the mole fraction of[HPy][BF_(4)],the first peak of the RDFs of HA1-F decreases,while that of CT6-CT6 rises at first and then decreases.This indicates that the solvent molecules affect the polar and non-polar regions of[HPy][BF_(4)]differently.
文摘Simulation of a class of delay stochastic system with distributed parameter is discussed. Difference schemes for the numerical computation of delay stochastic system are obtained. The precision of the difference scheme and the efficiency of the difference scheme in simulation of delay stochastic system with distributed parameter are analyzed. Examples are given to illustrate the application of the method.
基金Project(IRT0853) supported by Changjiang Scholars and Innovative Research Team in UniversityProject(DB03086) supported by Talents Fund of Xi’an University of Architecture and TechnologyProject(50978213) supported by National Natural Science Foundation
文摘The improved weighted-least-square model was used for state simulation of water distribution networks. And DFP algorithm was applied to get the model solution. In order to fit DFP algorithm,the initial model was transformed into a non-constrained optimization problem using mass conservation. Then,through one dimensional optimization and scale matrix establishment,the feasible direction of iteration was obtained,and the values of state variables could be calculated. After several iterations,the optimal estimates of state variables were worked out and state simulation of water distribution networks was achieved as a result. A program of DFP algorithm is developed with Delphi 7 for verification. By running on a designed network,which is composed of 55 nodes,94 pipes and 40 loops,it is proved that DFP algorithm can quickly get the convergence. After 36 iterations,the root mean square of all nodal head errors is reduced by 90.84% from 5.57 to 0.51 m,and the maximum error is only 1.30 m. Compared to Marquardt algorithm,the procedure of DFP algorithm is more stable,and the initial values have less influences on calculation accuracy. Therefore,DFP algorithm can be used for real-time simulation of water distribution networks.
基金This project was supported by NSFC Project (60474047), (60334010) and GuangDong Province Natural Science Foundationof China(31406)and China Postdoctoral Science Foundation (20060390725).
文摘Decentralized robust stabilization problem of discrete-time fuzzy large-scale systems with parametric uncertainties is considered. This uncertain fuzzy large-scale system consists of N interconnected T-S fuzzy subsystems, and the parametric uncertainties are unknown but norm-bounded. Based on Lyapunov stability theory and decentralized control theory of large-scale system, the design schema of decentralized parallel distributed compensation （DPDC） fuzzy controllers to ensure the asymptotic stability of the whole fuzzy large-scale system is proposed. The existence conditions for these controllers take the forms of LMIs. Finally a numerical simulation example is given to show the utility of the method proposed.
基金This work was supported by the National Natural Science Foundation of China(11772024).
文摘An integrated simulation system for solar sail spacecraft with individually controllable elements(SSICE)is investigated in this paper,including the modelling of power management,thermal control,attitude control,umbra prediction,and orbit prediction subsystems.Considering the self-control and reactivity subsystems,an agent based method is applied to develop the subsystem models.Each subsystem is an individual agent component,which manages itself autonomously and reacts to the requirements from other agents.To reduce computing burden on a specified computer and improve the suitability and flexibility of the integrated simulation system,a distributed framework is employed in the system by deploying agent components on different computers.The data transmission among agents is based on the transmission control protocol/Internet protocol(TCP/IP).A practical example of sun pointing is used to test the operating effect of the integrated system and the working condition of subsystems.The simulation results verify that the integrated system has higher sun pointing accuracy,quicker dynamical response to variations of the lighting,attitude and temperature and fewer computing resources with effective and accurate subsystems.The integrated system proposed in this paper can be applied to solar sail design,operation,and mission planning.
文摘Considering the fact that the temperature distribution in furnace of a tangential fired pulverized coal boiler is difficult to be measured and monitored, two-stage numerical simulation method was put forward. First, multi-field coupling simulation in typical work conditions was carried out off-line with the software CFX-4.3, and then the expression of temperature profile varying with operating parameter was obtained. According to real-time operating parameters, the temperature at arbitrary point of the furnace can be calculated by using this expression. Thus the temperature profile can be shown on-line and monitoring for combustion state in the furnace is realized. The simul-(ation) model was checked by the parameters measured in an operating boiler, (DG130-9.8/540.) The maximum of relative error is less than 12% and the absolute error is less than 120℃, which shows that the proposed two-stage simulation method is reliable and able to satisfy the requirement of industrial application.
基金supported by the National Science Foundation for Young Scholars of China(6130123471401175)
文摘Multiple earth observing satellites need to communicate with each other to observe plenty of targets on the Earth together. The factors, such as external interference, result in satellite information interaction delays, which is unable to ensure the integrity and timeliness of the information on decision making for satellites. And the optimization of the planning result is affected. Therefore, the effect of communication delay is considered during the multi-satel ite coordinating process. For this problem, firstly, a distributed cooperative optimization problem for multiple satellites in the delayed communication environment is formulized. Secondly, based on both the analysis of the temporal sequence of tasks in a single satellite and the dynamically decoupled characteristics of the multi-satellite system, the environment information of multi-satellite distributed cooperative optimization is constructed on the basis of the directed acyclic graph（DAG）. Then, both a cooperative optimization decision making framework and a model are built according to the decentralized partial observable Markov decision process（DEC-POMDP）. After that, a satellite coordinating strategy aimed at different conditions of communication delay is mainly analyzed, and a unified processing strategy on communication delay is designed. An approximate cooperative optimization algorithm based on simulated annealing is proposed. Finally, the effectiveness and robustness of the method presented in this paper are verified via the simulation.
基金Project(2010AA065201)supported by the High Technology Research and Development Program of ChinaProject(2013zzts038)supported by the Fundamental Research Funds for the Central Universities of ChinaProject(ZB2011CBBCe1)supported by the Major Program for Aluminum Corporation of China Limited,China
文摘Numerical simulations of gas–liquid two-phase flow and alumina transport process in an aluminum reduction cell were conducted to investigate the effects of anode configurations on the bath flow, gas volume fraction and alumina content distributions. An Euler–Euler two-fluid model was employed coupled with a species transport equation for alumina content. Three different anode configurations such as anode without a slot, anode with a longitudinal slot and anode with a transversal slot were studied in the simulation. The simulation results clearly show that the slots can reduce the bath velocity and promote the releasing of the anode gas, but can not contribute to the uniformity of the alumina content. Comparisons of the effects between the longitudinal and transversal slots indicate that the longitudinal slot is better in terms of gas–liquid flow but is disadvantageous for alumina mixing and transport process due to a decrease of anode gas under the anode bottom surface. It is demonstrated from the simulations that the mixing and transfer characteristics of alumina are controlled to great extent by the anode gas forces while the electromagnetic forces(EMFs) play the second role.
基金supported by the National Key Research and Development Program of China (Grant No.2021YFC3001204)。
文摘The study of non-axisymmetric fuel dispersal and detonation can provide reference for the prevention of industrial cloud explosion accidents and the design of fuel air explosive(FAE).The concentration and detonation fields of 85 kg cylindrical and fan-shaped fuel are investigated by experiments and numerical simulations.A dynamic model of the whole process for fuel dispersal and detonation is built.The concentration distribution of fuel is used as the initial condition to calculate the detonation stage,thus solving the initial value problem of detonation field.The phase and component changes of fuel cloud at different locations are compared.The fuel cloud is divided into directions of 0°,90°,135°and 180°.The results show that the maximum cloud radius is 20.94 m in 135°and the minimum is 12.04 m in 0°.The diameter of the detonation fireball is 53.6 m,and the peak temperature is 3455 K.The highest peak overpressure is 3.44 MPa in 0°and the lowest is 2.97 MPa in 135°.The proportion of liquid phase in 0°is22.90%,and the fuel loss is 11.8% and 9% higher than that in 135°and cylindrical charge,respectively.The stable propagation distance of blast wave in 135°is 42.50% longer than 0°and 28.37% longer than cylindrical charge.
文摘The study of the electric field around a surge arrester is useful for design procedures and diagnostic tests. The current work com- putes the electric field around a medium voltage gapless surge arrester using 2D and 3D representation of the arrester. The 2D simulation design, which is described in IEC 60099-4 Standard, cannot include the non symmetrical parts of the arrester geometry and the test arrange- ment. 3D simulation procedures have the advantage that takes into account these asymmetries, giving more accurate results for each measurement position. In order to confirm the suitability of the created models, the simulation results of the electric field, using the 2D and 3D edition of PC Opera, are compared with recorded measurements, which are obtained in laboratory using appropriate calibrated field meters.
文摘Risk quantification in grade is critical for mine design and planning.Grade uncertainty is assessed using multiple grade realizations,from geostatistical conditional simulations,which are effective to evaluate local or global uncertainty by honouring spatial correlation structures.The sequential Gaussian conditional simulation was used to assess uncertainty of grade estimates and illustrate simulated models in Sivas gold deposit,Turkey.In situ variability and risk quantification of the gold grade were assessed by probabilistic approach based on the sequential Gaussian simulations to yield a series of conditional maps characterized by equally probable spatial distribution of the gold grade for the study area.The simulation results were validated by a number of tests such as descriptive statistics,histogram,variogram and contour map reproductions.The case study demonstrates the efficiency of the method in assessing risk associated with geological and engineering variable such as the gold grade variability and distribution.The simulated models can be incorporated into exploration,exploitation and scheduling of the gold deposit.
文摘In order to study the movement of the long-distance torpedo-like autonomous underwater vehicle(AUV)which is controlled by the dynamic positioning system(DPS),by adopting momentum theorem and the angular momentum theorem,the appropriate movement math model for the long-distance torpedo-like AUV has been built and the thrust of DPS is distributed.Several representative movements of AUV are simulated,such as transferring between two random points and pointing circumrotation movement.The simulation result is analyzed.It shows that DPS including five thrusters can control the AUV movement steadily at low velocity.
