The “Backward Looking” Effect in the Continuum Model Considering a New Backward Equilibrium Velocity Function.

In this paper, a new continuum traffic model is developed considering the backward-looking effect through a new positive backward equilibrium speed function. As compared with the conventional full velocity difference model, the backward equilibrium velocity function, which is largely acceptably grounded from mathematical and physical perspectives, plays an important role in significantly enhancing the stability of the traffic flow field. A linear stability condition is derived to demonstrate the flow neutralization capacity of the model, whereas the Korteweg–de Vries–Burgers equation and the attendant analytical solution are deduced using nonlinear analysis to observe the traffic flow behavior near the neutral stability condition. A numerical simulation, used to determine the flow stability enhancement efficiency of the model, is also conducted to verify the theoretical results.

The “Backward Looking” Effect in the Continuum Model Considering a New Backward Equilibrium Velocity Function

In this paper, a new continuum traffic model is developed considering the backward-looking effect through a new positive backward equilibrium speed function. As compared with the conventional full velocity difference model, the backward equilibrium velocity function, which is largely acceptably grounded from mathematical and physical perspectives, plays an important role in significantly enhancing the stability of the traffic flow field. A linear stability condition is derived to demonstrate the flow neutralization capacity of the model, whereas the Korteweg–de Vries–Burgers equation and the attendant analytical solution are deduced using nonlinear analysis to observe the traffic flow behavior near the neutral stability condition. A numerical simulation, used to determine the flow stability enhancement efficiency of the model, is also conducted to verify the theoretical results.

Simulasi Numerik Model Matematika Arus Lalu Lintas Berbasis Fungsi Velositas Underwood

Abstrak.Model matematika arus lalu lintas pertama kali dikembangkan oleh Lighthill, Whitham dan Richards pada tahun 1956 yang dikenal dengan model (LWR). Dalam model LWR, fungsi kecepatan adalah unsur yang terpenting. Dalam makalah ini digunakan fungsi kecepatan underwood karena memiliki tingkat kesesuaian yang terbaik dibadingkan dengan fungsi kecepatan lainnya. Metode beda hingga implisit digunakan untuk menemukan solusi numerik model LWR dengan model kecepatan Underwood. Konvergensi metode beda hingga implisit dibuktikan dengan menggunakan teorema Ekuivalensi Lax. Simulasi numerik jalan raya satu lajur sepanjang 10 km dilakukan selama 1 jam menggunakan metode beda hingga implisit berdasarkan data awal dan batas yang dibuat secara artifisial. Simulasi numerik dilakukan dengan dua parameter berbeda. Hasil eksperimen menujukkan bahwa semakin tinggi rata-rata kepadatan kendaraan pada suatu laju mengakibatkan rata-rata kecepatan kendaraan akan berkurang. Kata kunci: Metode Beda Hingga Implisit, Model LWR, Arus Lalu Lintas, Fungsi Felositas Underwood, Simulasi Numerik.Kata kunci : Abstract. Mathematical traffic flow model was first developed by Lighthill, Whitham and Richards in 1956, known as (LWR) model. In LWR model, velocity function was most important. In this paper, Underwood velocity function was used. Implicit finite difference method used to found the numerical solution of LWR model with Underwood velocity model. Convergence the implicit finite difference method proved using the Lax equivalence theorem. The numerical simulation of 10 km highway of single lane was performed for 1 hours using the implicit finite difference method based on artificially generated initial and boundary data. Numerical simulation performed with two different parameters. An experimental result for the stability condition of the numerical scheme was also presented. Density, velocity, and fluks for 1 hours was experimental result of numerical simulation.Keywords: Implicit finite difference method, Lax equivalence theorem, LWR model, Traffic flow, Under-wood velocity Function, Numerical simulation.

Globally visible singularity in an astrophysical setup

The global visibility of a singularity as an end state of the gravitational collapse of a spherically symmetric pressureless cloud is investigated. We show the existence of a non-zero measured set of parameters: the total mass and the initial mean density of the collapsing cloud, giving rise to a physically strong globally visible singularity as the end state for a fixed velocity function. The existence of such a set indicates that such singularity is stable under small perturbation in the initial data causing its existence. This is true for marginally as well as non-marginally bound cases. The possibility of the presence of such suitable parameters in the astrophysical setup is then studied: 1) The singularities’ requirements at the center of the M87 galaxy and at the center of our galaxy (SgrA*) to be globally visible are discussed in terms of the initial size of the collapsing cloud forming them, presuming that such singularities are formed due to gravitational collapse. 2) The requirement for the primordial singularities formed due to a collapsing configuration after getting detached from the background universe, at the time of matter-dominated era just after the time of matter-radiation equality, to be globally visible, is discussed. 3) The scenario of the collapse of a neutron star after reaching a critical mass, which is achieved by accreting the supernova ejecta expelled by its binary companion core progenitor, is considered. The primary aim of this paper is to show that globally visible singularities can form in astrophysical setups under appropriate circumstances.

An Improved Car-Following Model considering Desired Safety Distance and Heterogeneity of Driver’s Sensitivity

We investigate the dynamic performance of traffic flow using a modified optimal velocity car-following model. In the car-following scenarios, the following vehicle must continuously adjust the following distance to the preceding vehicle in real time. A new optimal velocity function incorporating the desired safety distance instead of a preset constant is presented first to describe the abovementioned car-following behavior dynamically. The boundary conditions of the new optimal velocity function are theoretically analyzed. Subsequently, we propose an improved car-following model by combining the heterogeneity of driver’s sensitivity based on the new optimal velocity function and previous car-following model. The stability criterion of the improved model is obtained through the linear analysis method. Finally, numerical simulation is performed to explore the effect of the desired safety distance and the heterogeneity of driver’s sensitivity on the traffic flow. Results show that the proposed model has considerable effects on improving traffic stability and suppressing traffic congestion. Furthermore, the proposed model is compatible with the heterogeneity of driver’s sensitivity and can enhance the average velocity of traffic flow compared with the conventional model. In conclusion, the dynamic performance of traffic flow can be improved by considering the desired safety distance and the heterogeneity of driver’s sensitivity in the car-following model.

Flow of Micropolar Fluid Between Two Parallel Plates with Different Periodic Suction and Injection

The unsteady stokes flow of incompressible micropolar fluid between two porous plates is considered. The lower plate is subjected to periodic suction and different periodic injection is applied at the upper plate. Stream function for the flow is obtained and the variation of velocity function f  & g with  is shown graphically. The effects of the dimensionless parameters p, frequency parameter pt , micropolarity parameter pl and the microrotation parameter pj on the velocity functions f  and microrotation velocity function g are discussed and shown through the graphs.

The H i velocity function: a test of cosmology or baryon physics?

Accurately predicting the shape of the H i velocity function (VF) of galaxies is regarded widely as a fundamental test of any viable dark matter model. Straightforward analyses of cosmological N-body simulations imply that the Λ cold dark matter (ΛCDM) model predicts an overabundance of low circular velocity galaxies when compared to observed H i VFs. More nuanced analyses that account for the relationship between galaxies and their host haloes suggest that how we model the influence of baryonic processes has a significant impact on H i VF predictions. We explore this in detail by modelling H i emission lines of galaxies in the shark semi-analytic galaxy formation model, built on the surfs suite of ΛCDM N-body simulations. We create a simulated ALFALFA survey, in which we apply the survey selection function and account for effects such as beam confusion, and compare simulated and observed H i velocity width distributions, finding differences of ≲ 50 per cent, orders of magnitude smaller than the discrepancies reported in the past. This is a direct consequence of our careful treatment of survey selection effects and, importantly, how we model the relationship between galaxy and halo circular velocity – the H i mass–maximum circular velocity relation of galaxies is characterized by a large scatter. These biases are complex enough that building a VF from the observed H i linewidths cannot be done reliably.