Trapezoidal Flux Research Articles

Analysis of cell transmission model for traffic flow simulation with application to network traffic

The cell transmission model (CTM) is a macroscopic model that describes the dynamics of traffic flow over time and space. The effectiveness and accuracy of the CTM are discussed in this paper. First, the CTM formula is recognized as a finite-volume discretization of the kinematic traffic model with a trapezoidal flux function. To validate the constructed scheme, the simulation of shock waves and rarefaction waves as two important elements of traffic dynamics was performed. Adaptation of the CTM for intersecting and splitting cells is discussed. Its implementation on the road segment with traffic influx produces results that are consistent with the analytical solution of the kinematic model. Furthermore, a simulation on a simple road network shows the back and forth propagation of shock waves and rarefaction waves. Our numerical result agrees well with the existing result of Godunov’s finite-volume scheme. In addition, from this accurately proven scheme, we can extract information for the average travel time on a certain route, which is the most important information a traveller needs. It appears from simulations of different scenarios that, depending on the circumstances, a longer route may have a shorter travel time. Finally, there is a discussion on the possible application for traffic management in Indonesia during the Eid al-Fitr exodus. doi:10.1017/S1446181121000080

ANALYSIS OF CELL TRANSMISSION MODEL FOR TRAFFIC FLOW SIMULATION WITH APPLICATION TO NETWORK TRAFFIC

AbstractThe cell transmission model (CTM) is a macroscopic model that describes the dynamics of traffic flow over time and space. The effectiveness and accuracy of the CTM are discussed in this paper. First, the CTM formula is recognized as a finite-volume discretization of the kinematic traffic model with a trapezoidal flux function. To validate the constructed scheme, the simulation of shock waves and rarefaction waves as two important elements of traffic dynamics was performed. Adaptation of the CTM for intersecting and splitting cells is discussed. Its implementation on the road segment with traffic influx produces results that are consistent with the analytical solution of the kinematic model. Furthermore, a simulation on a simple road network shows the back and forth propagation of shock waves and rarefaction waves. Our numerical result agrees well with the existing result of Godunov’s finite-volume scheme. In addition, from this accurately proven scheme, we can extract information for the average travel time on a certain route, which is the most important information a traveller needs. It appears from simulations of different scenarios that, depending on the circumstances, a longer route may have a shorter travel time. Finally, there is a discussion on the possible application for traffic management in Indonesia during the Eid al-Fitr exodus.

Core Loss Modeling and Calculation for Trapezoidal Magnetic Flux Density Waveform

This article proposes a novel approach in order to understand the different kinds of core loss of the trapezoidal flux waveform. The proposed approach is based on the theory of magnetism and assessed with the experimental results to show that the total loss is composed of two terms: the effective triangular loss during the on-time resulting from the flux variation and the relaxation loss during the off-time, which is due to the magnetic after-effect phenomenon. The study shows that the relaxation loss depends on the off-time and it has a maximum at a particular off-time-to-on-time ratio that depends on the magnetic material. In addition to that, two models with accuracy higher than 96% and with a reduced number of parameters compared to the existing models are developed to predict the relaxation loss. The models are verified with previous experimental results and new experiments performed in this article.

An analytical method of calculating back-emf in dual consequent hybrid excitation synchronous machine

In order to solve the problem of asymmetric bidirectional flux control capability in hybrid excitation machine, a novel structure called dual consequent hybrid excitation synchronous (DCHES) machine is presented in this paper. Generally, the analysis of back-EMF for the machine with complex electromagnetic structure such as DCHES machine should utilize 3-D finite element analysis (FEA), which will require huge resources and computing time. In order to avoid using 3-D FEA to analyze the back-EMF of complex structure, an analytical method of calculating back-EMF is presented in this paper. The electromagnetic field in 3-D space can be simplified as a 2-D field by dividing the 3-D field into several simple zones, the resultant effect equals to the summation of every single 2-D field's effect. According to electromagnetic theory, the analytical formula of back-EMF is obtained on the basis of Fourier series. The influence of main parameters on back-EMF waveform under sine and trapezoidal flux distribution is discussed respectively. The theoretical result shows that the trapezoidal air-gap flux distribution would generate a sine back-EMF. Finally, the presented analytical method is verified and evaluated with experimental results.

Flow Dynamics and Plasma Heating of Spheromaks in SSX

We report several new experimental results related to flow dynamics and heating from single dipole-trapped spheromaks and spheromak merging studies at SSX. Single spheromaks (stabilized with a pair of external coils, see Brown, Phys. Plasmas 13 102503 (2006)) and merged FRC-like configurations (see Brown, Phys. Plasmas 13, 056503 (2006)) are trapped in our prolate (R = 0.2 m, L = 0.6 m) copper flux conserver. Local spheromak flow is studied with two Mach probes (r 1 ≤ ρ i , r 2 ≥ ρ i ) calibrated by time-of-flight with a fast set of magnetic probes at the edge of the device. Both Mach probes feature six ion collectors housed in a boron nitride sheath. The larger Mach probe will ultimately be used in the MST reversed field pinch. Line averaged flow is measured by ion Doppler spectroscopy (IDS) at the midplane. The SSX IDS instrument measures with 1 μs or better time resolution the width and Doppler shift of the C III impurity (H plasma) 229.7 nm line to determine the temperature and line-averaged flow velocity (see Cothran, RSI 77, 063504 (2006)). We find axial flows up to 100 km/s during formation of the dipole trapped spheromak. Flow returns at the wall to form a large vortex. Recent high-resolution IDS velocity measurements during spheromak merging show bi-directional outflow jets at ±40 km/s (nearly the Alfven speed). We also measure T i ≥ 80 eV and T e ≥ 20 eV during spheromak merging events after all plasma facing surfaces are cleaned with helium glow discharge conditioning. Transient electron heating is inferred from bursts on a four-channel soft x-ray array. The spheromaks are also characterized by a suite of magnetic probe arrays for magnetic structure B(r,t), and interferometry for n e . Finally, we are designing a new oblate, trapezoidal flux conserver for FRC studies. Equilibrium and dynamical simulations suggest that a tilt-stable, oblate FRC can be formed by spheromak merging in the new flux conserver.

Characterisation of nonoriented electric alloys under nonconventional conditions

The variations of magnetic and loss characteristics of nonoriented cobalt-iron and silicon-iron sheets have been investigated using an Epstein frame. Cobalt-iron alloys have been tested under sinusoidal magnetic flux density with respect to frequency and temperature. Both kinds of alloys have also been investigated with respect to frequency, time constant wavefront and temperature under trapezoidal flux density. The qualitative behaviour is identical under both flux density conditions for all these alloys. These investigations have made it possible to model the variations of iron losses with experimental parameters, except the temperature. These quantitative evolutions differ with alloy and flux-density conditions and do not confirm several propositions of different authors.

Power losses under sinusoidal, trapezoidal and distorted induction waveform

A setup has been developed by which one can measure magnetic power losses under arbitrary induction waveforms in the frequency range 1 Hz<f/sub m/<100 kHz. Selected results concerning sinusoidal, trapezoidal, and distorted waveforms investigated in grain-oriented, nonoriented, and amorphous laminations are reported. The role of the excess energy loss component, which is found to approximate to a good degree a f/sub m//sup 1/2/ law in the five-decade f/sub m/ range investigated, is emphasized. The results are discussed in the framework of a general theoretical approach in which the hysteresis, the classical and excess loss components, and their specific law of dependence on the instantaneous induction derivative are considered separately. A formulation for total power losses under arbitrary induction waveform is provided and applied, in good agreement with experiments, to the case of distortion introduced by the third-harmonic component. Loss under trapezoidal flux is predicted through a simplified analytical approach.<<ETX>>