Numerical analysis for viscoelastic fluid flow with distributed/variable order time fractional Maxwell constitutive models

Fractional calculus has been widely used to study the flow of viscoelastic fluids recently,and fractional differential equations have attracted a lot of attention.However,the research has shown that the fractional equation with constant order operators has certain limitations in characterizing some physical phenomena.In this paper,the viscoelastic fluid flow of generalized Maxwell fluids in an infinite straight pipe driven by a periodic pressure gradient is investigated systematically.Consider the complexity of the material structure and multi-scale effects in the viscoelastic fluid flow.The modified time fractional Maxwell models and the corresponding governing equations with distributed/variable order time fractional derivatives are proposed.Based on the L1-approximation formula of Caputo fractional derivatives,the implicit finite difference schemes for the distributed/variable order time fractional governing equations are presented,and the numerical solutions are derived.In order to test the correctness and availability of numerical schemes,two numerical examples are established to give the exact solutions.The comparisons between the numerical solutions and the exact solutions have been made,and their high consistency indicates that the present numerical methods are effective.Then,this paper analyzes the velocity distributions of the distributed/variable order fractional Maxwell governing equations under specific conditions,and discusses the effects of the weight coefficient(α)in distributed order time fractional derivatives,the orderα(r,t)in variable fractional order derivatives,the relaxation timeλ,and the frequencyωof the periodic pressure gradient on the fluid flow velocity.Finally,the flow rates of the distributed/variable order fractional Maxwell governing equations are also studied.

A Class of Single Machine Scheduling Problems with Variable Processing Time

In this paper, single machine scheduling problems with variable processing time are raised. The criterions of the problem considered are minimizing scheduling length of all jobs, flow time and number of tardy jobs and so on. The complexity of the problem is determined. [WT5HZ]

An On-Line Modeling Based Kalman Filtering Process for Time-Interval-Variable Sequences with Application to Astronomic Surveying

The problem of variable sampling time interval which appears in application of Kalman Filtering is analyzed and the corresponding filtering process with or without present transition matrix is suggested, then an application experiment for astronomical surveying is introduced. In this process, the known stochastically variable sampling time intervals play the roles as deterministic input sequences of the state-space description, and the corresponding matrix and (if needed) state transition matrix can be established by performing real-time and structure-linear system identification.

Strong NP-Hardness of Single Machine Scheduling Problems with Variable Processing Time

In this paper, single machine scheduling problems with variable processing time is discussed according to published instances of management engineering. Processing time of a job is the product of a “coefficient' of the job on position i and a “normal' processing time of the job. The criteria considered is to minimize scheduled length of all jobs. A lemma is proposed and proved. In no deadline constrained condition, the problem belongs to polynomial time algorithm. It is proved by using 3 partition that if the problem is deadline constrained, its complexity is strong NP hard. Finally, a conjuncture is proposed that is to be proved.

Adaptive path planning for unmanned aerial vehicles based on bi-level programming and variable planning time interval

This paper presents an adaptive path planner for unmanned aerial vehicles （UAVs） to adapt a real-time path search procedure to variations and fluctuations of UAVs’ relevant performances, with respect to sensory capability, maneuverability, and flight velocity limit. On the basis of a novel adaptability-involved problem statement, bi-level programming （BLP） and variable planning step techniques are introduced to model the necessary path planning components and then an adaptive path planner is developed for the purpose of adaptation and optimization. Additionally, both probabilistic-risk-based obstacle avoidance and performance limits are described as path search constraints to guarantee path safety and navigability. A discrete-search-based path planning solution, embedded with four optimization strategies, is especially designed for the planner to efficiently generate optimal flight paths in complex operational spaces, within which different surface-to-air missiles （SAMs） are deployed. Simulation results in challenging and stochastic scenarios firstly demonstrate the effectiveness and efficiency of the proposed planner, and then verify its great adaptability and relative stability when planning optimal paths for a UAV with changing or fluctuating performances.

发动机可变气门正时阀的微分先行的PID控制算法

为优化发动机可变气门正时(VVT)阀原有的控制,提出了微分先行的比例积分微分(PID)控制算法。分析了VVT阀的工作原理与机械结构,测定了VVT阀的关键参数。建立了数学模型与Simulink仿真模型,借助于Matlab/Simulink平台。用实机平台与仿真平台,验证所提出的控制算法。结果表明:在VVT阀控制中,面对目标期望值的波动,与传统PID算法相比,在阶跃测试时,微分先行PID算法超调量降低0.8%,静态误差降低0.15%;在追踪测试时,其超调量降低1%,静态误差降低0.15%。因此,本算法完成了对VVT阀的优化控制。

Interval Type-2 Fuzzy Hierarchical Adaptive Cruise Following-Control for Intelligent Vehicles

Intelligent vehicles can effectively improve traffic congestion and road traffic safety.Adaptive cruise followingcontrol(ACFC)is a vital part of intelligent vehicles.In this paper,a new hierarchical vehicle-following control strategy is presented by synthesizing the variable time headway model,type-2 fuzzy control,feedforward+fuzzy proportion integration(PI)feedback(F+FPIF)control,and inverse longitudinal dynamics model of vehicles.Firstly,a traditional variable time headway model is improved considering the acceleration of the lead car.Secondly,an interval type-2 fuzzy logic controller(IT2 FLC)is designed for the upper structure of the ACFC system to simulate the driver's operating habits.To reduce the nonlinear influence and improve the tracking accuracy for the desired acceleration,the control strategy of F+FPIF is given for the lower control structure.Thirdly,the lower control method proposed in this paper is compared with the fuzzy PI control and the traditional method(no lower controller for tracking desired acceleration)separately.Meanwhile,the proportion integration differentiation(PID),linear quadratic regulator(LQR),subsection function control(SFC)and type-1 fuzzy logic control(T1 FLC)are respectively compared with the IT2 FLC in control performance under different scenes.Finally,the simulation results show the effectiveness of IT2 FLC for the upper structure and F+FPIF control for the lower structure.

Modeling of seasonal soil cold storage using natural cold energy

To reduce energy consumption on summer air conditioning,a novel seasonal soil cold storage mode using natural energy is presented and two-dimensional transient heat transfer model of U-tube is developed. The three processes of cold storage in winter,shut-down in transition season and cold extraction in summer are simulated by using sensitive heat capacity method with variable time step. The changing of U-tube outlet water temperature in different periods,daily cold storage and cold extraction are estimated. The temperature field of the U-tube and soil around the tube is investigated. Simulations show that seasonal soil cold storage using natural cold energy is feasible in the north to Changchun,which provides theoretical support for seasonal soil cold storage application.

Monitoring of Soil Bulk Density in Context with Its Small-Scale Spatial Heterogeneity

The main aim of soil monitoring system is to obtain the knowledge of the most current state and development of soil properties according to concrete threats to soil. To determine the significant changes of soil properties in time, it is important to know spatial variability of concrete soil parameter for concrete site. Only those time changes of the soil parameter are significant, which exceed its spatial variability at the site. The main aim of the study has been focused on the evaluation of small-scale site heterogeneity of equilibrium soil bulk density and the integration of impact of this heterogeneity in evaluation of degradation process of soil compaction in time. As site variation coefficients have considerably varied at standard sampling with five repetitions during monitoring period, one-time detail spatial variability mapping of soil bulk density was realized at 17 repetitions on five selected monitoring sites with different soil type, texture and use. This increase in the number of sampling points helped us to specify and stabilize the values of variation coefficients (between minimum and maximum by standard sampling) as well as the extent of confidence intervals. Standard deviations at the chosen monitoring sites moved from 0.039 to 0.118 g·cm-3 in topsoil and from 0.031 to 0.067 g·cm-3 in subsoil and expressed as variation coefficient 2.9% - 9.2% and 2.0% - 4.9%, respectively. The intervals of significant time changes of soil bulk density for the sites and depths were determined on the base of its site confidence interval (95%) and uncertainty rate of its measure methodology. The time changes of bulk density values between single year-to-year sampling were overlapped by this interval of significant changes to obtain significant bulk density changes in time. This method allowed us to distinguish significant time changes in soil bulk density from insignificant ones. The bulk density value changes on the monitoring sites were significant in the range of six to nine years within observed period 2002-2014 in both depths.

Is the kinematics of special relativity incomplete?

A thorough analysis of composite inertial motion (relativistic sum) within the framework of special relativity leads to the conclusion that every translational motion must be the symmetrically composite relativistic sum of a finite number of quanta of velocity. It is shown that the resulting spacetime geometry is Gaussian and the four-vector calculus to have its roots in the complex-number algebra. Furthermore, this results in superluminality of signals travelling at or nearly at the canonical velocity of light between rest frames even if resting to each other.

Modeling relationships between the network distance and travel time dynamics for assessing equity of accessibility to urban parks

Static models of accessibility are usually based on the fixed distance or Average Travel Time(ATT)models.Because of ignoring the traffic as a dynamic process affecting the accessibility through the change of Travel Time(TT),these models lead to unperceived temporal inequities.In contrast to the consideration of the temporal Variation of TT(VTT)in the previous studies,the variation of traffic-related TT and its relations with network distance has not been considered.In this study,relations between VTT and network distance to access urban parks in Tehran megacity has been modeled.Traffic maps at five times of day are used to produce TT maps of Traffic Analysis Zones(TAZs)to their 3-closest parks.Comparison of the Gini coefficients of accessibility show significant inequities of accessibility at different times of day.Relations between the distance,ATT,and TT_(max) are modeled by statistical analysis.Results show both TT and TTmax have significant positive relations with distance and traffic and reach their maximum at 6 p.m.Observation of significant relations between distance,ATT,TT_(max),and VTT provides interesting knowledge for the conversion of temporal measures of equity(TT)to a physical measure of equity(distance).A simple application of these findings for effective management of the spatiotemporal inequities is the definition of critical distances from public services.As an example,to decrease the TT_(max) of TAZs to less than 12 min,their maximum distance to the closest parks should be less than 4 km.The developed approach can be adopted for the accessibility evaluation of the other public services,particularly the health and education centers.

THE OPTICAL VARIABILITY ON A SHORT TIME SCALE OF 6 BL LAC OBJECTS

Ⅰ. INTRODUCTION BL Lac objects were the prototype of a new class of astrophysically interested objects with these peculiar characteristies: (ⅰ) Absence of emission lines in the core source;(ⅱ) rapid variability at radio, IR and visual wavelengths; (ⅲ) non-thermal

Design of a hybrid magnetomotive force electromechanical valve actuator

We propose a novel axis-symmetric modified hybrid permanent magnet(PM)/electromagnet(EM) magnetomotive force actuator for a variable valve timing camless engine. The design provides a large magnetic force with low energy consumption, low coil inductance, PM demagnetization isolation, and improved transient response. Simulation and experimental results confirm forces of about 200 N(in the presence of coil current) at the equilibrium position and 500 N(in the absence of coil current) at the armature seat. We compared our proposed design with a double solenoid valve actuator(DSVA). The finite element method(FEM) designs of the DSVA and our proposed valve actuator were validated by experiments performed on manufactured prototypes.

Adaptive Stabilization of Neural Control for Robot Trajectory Tracking

A neural network (NN) based adaptive control law is proposed for the tracking control of an n link robot manipulator with unknown dynamic nonlinearities. Basis function like nets are employed to approximate the plant nonlinearities, and the bound on the NN reconstruction error is assumed to be unknown. The proposed NN based adaptive control approach integrates an NN approach with an adaptive implementation of discrete variable structure control with a simple estimation law to estimate the upper bound on the NN reconstruction error and an additional control input to be updated as a function of the estimate. Lyapunov stability theory is used to prove the uniform ultimate boundedness of the tracking error.