Treatment of Polio Delayed Epidemic Model via Computer Simulations

Through the study,the nonlinear delayed modelling has vital significance in the different field of allied sciences like computational biology,computational chemistry,computational physics,computational economics and many more.Polio is a contagious viral illness that in its most severe form causes nerve injury leading to paralysis,difficulty breathing and sometimes death.In recent years,developing regions like Asia,Africa and sub-continents facing a dreadful situation of poliovirus.That is the reason we focus on the treatment of the polio epidemic model with different delay strategies in this article.Polio delayed epidemic model is categorized into four compartments like susceptible,exposed,infective and vaccinated classes.The equilibria,positivity,boundedness,and reproduction number are investigated.Also,the sensitivity of the parameters is analyzed.Well,known results like the Routh Hurwitz criterion and Lyapunov function stabilities are investigated for polio delayed epidemic model in the sense of local and global respectively.Furthermore,the computer simulations are presented with different traditions in the support of the analytical analysis of the polio delayed epidemic model.

Comparison of Passive Control Methods on Cavity Aeroacoustic Using Delayed Detached Eddy Simulation

Delayed detached eddy simulation(DDES)is performed to investigate an open cavity at Ma0.85.Clean cavity and cavity with leading-edge saw tooth spoiler and flattop spoiler,are modeled.The results obtained from clean cavity prediction are compared with experimental sound pressure level(SPL)data from QinetiQ,UK.DDES results agree well with the experimental data.Furthermore,comparisons are made with the predicted SPL between the three configurations to find out the effect of different passive control methods.Both the spoilers can suppress the over-all SPL up to 8dB.The main focuses of this investigation are to exam the DDES method on cavity aeroacoustic analysis and test the noise suppression effect by saw tooth spoiler and flattop spoiler.

Detached-eddy Simulation for Time-dependent Turbulent Cavitating Flows

The Reynolds-averaged Navier-Stokes（RANS）,such as the original k-ω two-equation closures,have been very popular in providing good prediction for a wide variety of flows with presently available computational resource.But for cavitating flows,the above equations noticeably over-predict turbulent production and hence effective viscosity.In this paper,the detached eddy simulation（DES） method for time-dependent turbulent cavitating flows is investigated.To assess the state-of-the-art of computational capabilities,different turbulence models including the widely used RANS model and DES model are conducted.Firstly,in order to investigate the grid dependency in computations,different grid sizes are adopted in the computation.Furthermore,the credibility of DES model is supported by the unsteady cavitating flows over a 2D hydrofoil.The results show that the DES model can effectively reduce the eddy viscosities.From the experimental validations regarding the force analysis,frequency and the unsteady cavity visualizations,more favorable agreement with experimental visualizations and measurements are obtained by DES model.DES model is better able to capture unsteady phenomena including cavity length and the resulting hydrodynamic characteristics,reproduces the time-averaged velocity quantitatively around the hydrofoil,and yields more acceptable and unsteady dynamics features.The DES model has shown to be effective in improving the overall predictive capability of unsteady cavitating flows.

A Novel Strategy for Simulating the Main Fractionator of Delayed Cokers by Separating the De-superheating Process

Delayed coking is an important process in refinery to convert heavy residue oils from crude distillation units （CDUs） and fluid catalytic cracking units （FCCUs） into dry gas, liquefied petroleum gas （LPG）, gasoline, die- sel, gas oils and cokes. The main fractionator, separating superheating reaction vapors from the coke drums into lighter oil products, involves a de-superheating section and a rectifying section, and couldn＇t be simulated as a whole column directly because of non-eouilibrium in the de-suoerheatine section. It is verv imoortant to correctlv simulate the main fractionator for operational parameter and energy-use optimization of delayed cokers. This paper discusses the principle of de-superheating processes, and then proposes a new simulation strategy. Some key issues such as composition prediction of the reaction vapors, selection of thermodynamic methods, estimation of tray efficiency, etc. are discussed. The proposed simulation approach is applied to two industrial delayed cokers with typical technological processes in a Chinese refinery by using PRO/II. The simulation results obtained are well consistent with the actual operation data, which indicates that the presented approach is suitable to simulate the main fraction- ators of delayed cokers or other distillation columns consisting of de-superheating sections and rectifying sections.

A simulation model for estimating train and passenger delays in large-scale rail transit networks

A simulation model was proposed to investigate the relationship between train delays and passenger delays and to predict the dynamic passenger distribution in a large-scale rail transit network. It was assumed that the time varying original-destination demand and passenger path choice probability were given. Passengers were assumed not to change their destinations and travel paths after delay occurs. CapaciW constraints of train and queue rules of alighting and boarding were taken into account. By using the time-driven simulation, the states of passengers, trains and other facilities in the network were updated every time step. The proposed methodology was also tested in a real network, for demonstration. The results reveal that short train delay does not necessarily result in passenger delays, while, on the contrary, some passengers may get benefits from the short delay. However, large initial train delay may result in not only knock-on train and passenger delays along the same line, but also the passenger delays across the entire rail transit network.

Detached-eddy simulation of flow around high-speed train on a bridge under cross winds

In order to describe an investigation of the flow around high-speed train on a bridge under cross winds using detached-eddy simulation(DES), a 1/8th scale model of a three-car high-speed train and a typical bridge model are employed, Numerical wind tunnel technology based on computational fluid dynamics(CFD) is used, and the CFD models are set as stationary models. The Reynolds number of the flow, based on the inflow velocity and the height of the vehicle, is 1.9×10~6. The computations are conducted under three cases, train on the windward track on the bridge(WWC), train on the leeward track on the bridge(LWC) and train on the flat ground(FGC). Commercial software FLUENT is used and the mesh sensitivity research is carried out by three different grids: coarse, medium and fine. Results show that compared with FGC case, the side force coefficients of the head cars for the WWC and LWC cases increases by 14% and 29%, respectively; the coefficients of middle cars for the WWC and LWC increase by 32% and 10%, respectively; and that of the tail car increases by 45% for the WWC whereas decreases by 2% for the LWC case. The most notable thing is that the side force and the rolling moment of the head car are greater for the LWC, while the side force and the rolling moment of the middle car and the tail car are greater for the WWC. Comparing the velocity profiles at different locations, the flow is significantly influenced by the bridge-train system when the air is close to it. For the three cases(WWC, LWC and FGC), the pressure on the windward side of train is mostly positive while that of the leeward side is negative. The discrepancy of train's aerodynamic force is due to the different surface area of positive pressure and negative pressure zone. Many vortices are born on the leeward edge of the roofs. Theses vortices develop downstream, detach and dissipate into the wake region. The eddies develop irregularly, leading to a noticeably turbulent flow at leeward side of train.

Analysis of actuator delay and its effect on uncertainty quantification for real-time hybrid simulation

Uncertainties in structure properties can result in different responses in hybrid simulations. Quantification of the effect of these tmcertainties would enable researchers to estimate the variances of structural responses observed from experiments. This poses challenges for real-time hybrid simulation （RTHS） due to the existence of actuator delay. Polynomial chaos expansion （PCE） projects the model outputs on a basis of orthogonal stochastic polynomials to account for influences of model uncertainties. In this paper, PCE is utilized to evaluate effect of actuator delay on the maximum displacement from real-time hybrid simulation of a single degree of freedom （SDOF） structure when accounting for uncertainties in structural properties. The PCE is first applied for RTHS without delay to determine the order of PCE, the number of sample points as well as the method for coefficients calculation. The PCE is then applied to RTHS with actuator delay. The mean, variance and Sobol indices are compared and discussed to evaluate the effects of actuator delay on uncertainty quantification for RTHS. Results show that the mean and the variance of the maximum displacement increase linearly and exponentially with respect to actuator delay, respectively. Sensitivity analysis through Sobol indices also indicates the influence of the single random variable decreases while the coupling effect increases with the increase of actuator delay.

Simulation of a class of delay stochastic system with distributed parameter

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.

Numerical simulation of the delay arming process of initiating explosive brakes

The delay arming process of initiating explosive （ IE ） brakes for fuse is complex and hard to be verified. A numerical simulation model of IE brakes was established based on the arbitrary La- grange-Euler method. The model included the structure, the air filed, etc. The simulation boundary conditions were defined, including the contacts, blasting parameters of the explosive and the fluid- solid coupling interface. The simulation results show that the shear pin of the chosen IE can be cut off. When the piston needs to move 0.8 cm, the time set to the delay arming of the IE brakes model is about 40μS. The maximum displacement of the piston is 1. 17 cm. The model provides basis for parameters design and further improvement of IE brakes.

Theoretical and experimental studies on critical time delay of multi-DOF real-time hybrid simulation

This paper aims to investigate the critical stability of a multi-degree-of-freedom(multi-DOF)real-time hybrid simulation(RTHS).First,the critical time-delay analysis models are developed using the continuous-and discrete-time root locus(RL)techniques,respectively.A bilinear transform is introduced into the first-order Padéapproximation while conducting the discrete RL analysis.Based on this technique,the time delay can be explicitly used as the gain factor and thus the instability mechanism of the multi-DOF RTHS system can be analyzed.Subsequently,the critical time delays calculated by the continuous-and discrete-time RL techniques,respectively,are compared for a 2-DOF RTHS system.It is shown that assuming the RTHS system to be a continuous-time system will result in overestimating the critical time delay.Finally,theoretically calculated critical delays are demonstrated and validated by numerical simulation and a set of RTHS experiments.Parametric analysis provides a glimpse of the effects of time step,frequency and damping ratio in a performing partitioning scheme.The constructed analysis model proves to be useful for evaluating the critical time delay to predict stability and performance,therefore facilitating successful RTHS.

Comparison of delay compensation methods for real-time hybrid simulation using frequency-domain evaluation index

The delay compensation method plays an essential role in maintaining the stability and achieving accurate real-time hybrid simulation results. The effectiveness of various compensation methods in different test scenarios, however, needs to be quantitatively evaluated. In this study, four compensation methods （i.e., the polynomial extrapolation, the linear acceleration extrapolation, the inverse compensation and the adaptive inverse compensation） are selected and compared experimentally using a frequency evaluation index （FEI） method. The effectiveness of the FEI method is first verified through comparison with the discrete transfer fimction approach for compensation methods assuming constant delay. Incomparable advantage is further demonstrated for the FEI method when applied to adaptive compensation methods, where the discrete transfer function approach is difficult to implement. Both numerical simulation and laboratory tests with predefined displacements are conducted using sinusoidal signals and random signals as inputs. Findings from numerical simulation and experimental results demonstrate that the FEI method is an efficient and effective approach to compare the performance of different compensation methods, especially for those requiring adaptation of compensation parameters.

Complicated flow in tip flow field of a compressor tandem cascade using delayed detached eddy simulation

The complex flow characteristics in the tip region of a tandem cascade with tip clearance have been calculated and analyzed using Delayed Detached Eddy Simulation(DDES).The coherent mechanism of the vortex structures near the blade tip was discussed,and the unsteady behaviors and features in the tip flow field were analyzed.Additionally,the interaction between the tip leakage flow and the gap jet was revealed.The results show that,compared to the datum cascade,the blade tip load of the rear blade increases while that of the front blade decreases.Unsteady fluctuations of the tandem cascade are mainly caused by the interaction between the tip leakage flow and gap jet,and by the mixing of the vortex structures,but there is no essential change in the spectrum feature of the tip leakage flow.Finally,a detailed analysis of the development of vortices in the tip region is conducted by the topological structures of the flow field.Combined with the three-dimensional vortex structures,the schematic diagram of the vortex system of the datum single-row cascade and tandem cascade is summarized.

Detached-eddy simulation of supersonic turbulent flow over rearward facing step

Detailed formulation of the detached-eddy simulation （DES） based on shear stress transport model （SST） was deduced. Based on finite volume method, detached-eddy simulation of super- sonic turbulent flow over rearward facing step was conducted. Multi-block structured non-conform grid was designed. The obtained distribution of wall pressure coefficient along the downstream of the step was in good agreement with experiment. The structure of supersonic flow over rearward facing step is complicated and contains boundary layer-shock interaction, shock-shock interaction and sec- ondary flow separation. The predictions of the corner pressure and location of the reattachment shock are more exact than the Reynolds-averaged method. Results show that detached-eddy simulation can simulate the supersonic separated flows exactly and has advantages over Reynolds-averaged method. The partition of the detached-eddy simulation can be easily achieved by using multi-block non-conform grid, which reduces the requirement of the computational resources as well.

Research on service capacity of widened intersection based on traffic simulation

Delay analysis method is adopted to study the service capacity of a widened intersection. Traffic simulation software VISSIM is used for microscopic simulation of a widened intersection so as to obtain a delay curve. The delay-volume model of a widened intersection is established based on traffic simulation. The suggested value of basic service capacity of the widened left-turn lane is given along with how to determine correction factors and practical service capacity.

Applications of scale-adaptive simulation technique based on one-equation turbulence model

A modified scale-adaptive simulation （SAS） technique based on the Spalart- Allmaras （SA） model is proposed. To clarify its capability in prediction of the complex turbulent flow, two typical cases are carried out, i.e., the subcritical flow past a circular cylinder and the transonic flow over a hemisphere cylinder. For comparison, the same cases are calculated by the detached-eddy simulation （DES）, the delayed-detached eddy simulation （DDES）, and the XY-SAS approaches. Some typical results including the mean pressure coefficient, velocity, and Reynolds stress profiles are obtained and compared with the experiments. Extensive calculations show that the proposed SAS technique can give better prediction of the massively separated flow and shock/turbulent-boundary-layer interaction than the DES and DDES methods. Furthermore, by the comparison of the XY-SAS model with the present SAS model, some improvements can be obtained.

Global Stability Analysis of a Delayed SEIQR Epidemic Model with Quarantine and Latent

In this paper, we study a kind of the delayed SEIQR infectious disease model with the quarantine and latent, and get the threshold value which determines the global dynamics and the outcome of the disease. The model has a disease-free equilibrium which is unstable when the basic reproduction number is greater than unity. At the same time, it has a unique endemic equilibrium when the basic reproduction number is greater than unity. According to the mathematical dynamics analysis, we show that disease-free equilibrium and endemic equilibrium are locally asymptotically stable by using Hurwitz criterion and they are globally asymptotically stable by using suitable Lyapunov functions for any Besides, the SEIQR model with nonlinear incidence rate is studied, and the that the basic reproduction number is a unity can be found out. Finally, numerical simulations are performed to illustrate and verify the conclusions that will be useful for us to control the spread of infectious diseases. Meanwhile, the will effect changing trends of in system (1), which is obvious in simulations. Here, we take as an example to explain that.

Efficiency analysis of numerical integrations for finite element substructure in real-time hybrid simulation

Finite element（FE） is a powerful tool and has been applied by investigators to real-time hybrid simulations（RTHSs）. This study focuses on the computational efficiency, including the computational time and accuracy, of numerical integrations in solving FE numerical substructure in RTHSs. First, sparse matrix storage schemes are adopted to decrease the computational time of FE numerical substructure. In this way, the task execution time（TET） decreases such that the scale of the numerical substructure model increases. Subsequently, several commonly used explicit numerical integration algorithms, including the central difference method（CDM）, the Newmark explicit method, the Chang method and the Gui-λ method, are comprehensively compared to evaluate their computational time in solving FE numerical substructure. CDM is better than the other explicit integration algorithms when the damping matrix is diagonal, while the Gui-λ（λ = 4） method is advantageous when the damping matrix is non-diagonal. Finally, the effect of time delay on the computational accuracy of RTHSs is investigated by simulating structure-foundation systems. Simulation results show that the influences of time delay on the displacement response become obvious with the mass ratio increasing, and delay compensation methods may reduce the relative error of the displacement peak value to less than 5% even under the large time-step and large time delay.

Distributed cooperative task planning algorithm for multiple satellites in delayed communication environment

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.

Principle and key technology of generalized high precision simulation of TT&C channel

A generalized simulation method of the tracking,telemetry and control（TT＆C） channel,which is applicable to wideband and arbitrary radio frequency（RF） signal,is proposed.It can accurately simulate the dynamic transmission delay of the arbitrary RF signal in channels,especially regardless of any prior knowledge including signal form,signal parameters,and so on.The proposed method orthogonally demodulates the wideband and arbitrary RF signal to complex baseband by a known local oscillator（LO） signal.Whereafter,it takes measures to obtain the delay reconstruction signal of baseband signals based on the dynamic transmission delay between a ground station and a responder.Meanwhile,it manages to obtain the delay reconstruction signal of LO signals.The simulation output signal（the delayed RF signal） can be achieved through the synthesis of the two delay reconstruction signals mentioned above.The principle and its related key technology are described in detail,and the realizable system architecture is given.

A new integration scheme for application to seismic hybrid simulation

Hybrid simulation is a powerful test method for evaluating the seismic performance of structural systems. This method makes it feasible that only critical components of a structure be experimentally tested. This paper presents a newly proposed integration algorithm for seismic hybrid simulation which is aimed to extend its capabilities to a wide range of systems where existing methods encounter some limitations. In the proposed method, which is termed the variable time step （VTS） integration method, an implicit scheme is employed for hybrid simulation by eliminating the iterative phase on experimental element, the phase which is necessary in regular implicit applications. In order to study the effectiveness of the VTS method, a series of numerical investigations are conducted which show the successfulness of the VTS method in obtaining accurate, stable and converged responses. Then, in a comparative approach, the improved accuracy of the VTS method over commonly used integration methods is demonstrated. The stability of the VTS method is also studied and the results show that it provides conditional stability; however, its stability limit is well beyond the accuracy limit. The effect of time delay on the VTS method results is also investigated and it is shown that the VTS method is quite successful in handling this experimental error.