On Time-Dependent Trip Distance Distribution with For-Hire Vehicle Trips in Chicago

2021 ◽  
pp. 036119812110215
Author(s):  
Irene Martínez ◽  
Wen-Long Jin
Keyword(s):  
Probability Density ◽  
System Analysis ◽  
Space Dimension ◽  
Distance Distribution ◽  
Time Dependent ◽  
Demand Pattern ◽  
Departure Time ◽  
Trip Distance ◽  
New Space ◽  
Log Normal

For transportation system analysis in a new space dimension with respect to individual trips’ remaining distances, vehicle trips demand has two main components: the departure time and the trip distance. In particular, the trip distance distribution (TDD) is a direct input to the bathtub model in the new space dimension, and is a very important variable to consider in many applications, such as the development of distance-based congestion pricing strategies or mileage tax. For a good understanding of the demand pattern, both the distribution of trip initiation and trip distance should be calibrated from real data. In this paper, it is assumed that the demand pattern can be described by the joint distribution of trip distance and departure time. In other words, TDD is assumed to be time-dependent, and a calibration and validation methodology of the joint probability is proposed, based on log-likelihood maximization and the Kolmogorov–Smirnov test. The calibration method is applied to empirical for-hire vehicle trips in Chicago, and it is concluded that TDD varies more within a day than across weekdays. The hypothesis that TDD follows a negative exponential, log-normal, or Gamma distribution is rejected. However, the best fit is systematically observed for the time-dependent log-normal probability density function. In the future, other trip distributions should be considered and also non-parametric probability density estimation should be explored for a better understanding of the demand pattern.

Time-dependent electric field effect on the photodetachment dynamics of negative ions

2017 ◽  
Vol 95 (5) ◽  
pp. 507-513 ◽  
Author(s):  
De-hua Wang
Keyword(s):  
Electric Field ◽  
Probability Density ◽  
External Electric Field ◽  
Negative Ions ◽  
Time Dependent ◽  
Negative Ion ◽  
Electric Field Effect ◽  
Electron Trajectories ◽  
Oscillatory Pattern ◽  
Electron Probability Density

This paper addresses the photodetachment dynamics of a negative ion in a time-dependent electric field based on the semiclassical open-orbit theory. The photodetached electron probability density in a real time domain is studied in a gradient electric field for the first time. It is found that because of the influence of the gradient electric field, two or more electron trajectories can arrive at a given point on the detector, and the interference effect between these electron trajectories causes oscillatory structures in the electron probability density. Our calculation results suggest that when the external electric field changes very slowly with time, only two electron trajectories can arrive at a given point on the detector and the electron probability density exhibits a regular two-term oscillatory pattern. However, when the electric field changes quickly with time, four electron trajectories can reach the detector, which makes the oscillatory structures in the electron probability density become much more complicated. In addition, the electric field strength, photon energy, and the position of the detector can affect the electron probability density of this system sensitively. Our study provides a clear and intuitive picture for the photodetachment dynamics of the negative ion in the external electric field from a time-dependent viewpoint and may guide the future experimental researches on the photodetachment microscopy of negative ions in the time-dependent electric field.

The Joint Probability Density Function of the SSC Combiner Output Signal at two Time Instants in the Presence of Log-Normal Fading

1970 ◽  
Vol 109 (3) ◽  
pp. 11-16 ◽  
Author(s):  
D. S. Krstic ◽  
P. B. Nikolic ◽  
M. C. Stefanovic ◽  
F. Destovic
Keyword(s):  
Probability Density Function ◽  
Probability Density ◽  
Density Function ◽  
Output Signal ◽  
Joint Probability ◽  
Time Instant ◽  
Joint Probability Density Function ◽  
Decision Threshold ◽  
Log Normal ◽  
Joint Probability Density

In this paper the probability density function of the Switch and Stay Combiner (SSC) output signal at one time instant and the joint probability density function of the SSC combiner output signal at two time instants, in the presence of log-normal fading, are determined in the closed form expressions. The results are shown graphically for different variance values and decision threshold values. If the digital telecommunication systems work on the manner described in this paper, the error probability will be significantly reduced. Ill. 6, bibl. 24 (in English; abstracts in English and Lithuanian).http://dx.doi.org/10.5755/j01.eee.109.3.161

A probability density function method for turbulent mixing and combustion on three-dimensional unstructured deforming meshes

2000 ◽  
Vol 1 (2) ◽  
pp. 171-190 ◽  
Author(s):  
S Subramaniam ◽  
D. C. Haworth
Keyword(s):  
Probability Density Function ◽  
Probability Density ◽  
Density Function ◽  
Turbulent Mixing ◽  
Three Dimensional ◽  
Quantitative Agreement ◽  
Particle Number Density ◽  
Time Dependent ◽  
Ic Engine ◽  
Density Control

A hybrid Lagrangian-Eulerian methodology is developed for numerical simulation of turbulent mixing and combustion in arbitrary three-dimensional time-dependent geometric configurations. The context is a probability density function (PDF) based approach intended for modelling in cylinder processes in reciprocating piston internal combustion (IC) engines. Issues addressed include mean estimation, particle tracking and particle number-density control on three-dimensional unstructured deforming meshes. The suitability of the methodology for statistically time-dependent three-dimensional turbulent flow with large density variations is demonstrated via simulations of turbulent freon vapour/air mixing on an unstructured deforming mesh representing an idealized IC engine [13]. Computed profiles of mean and r.m.s. freon mole fractions show good quantitative agreement with measurements. Moreover, inherent advantages of the Lagrangian-Eulerian PDF approach are demonstrated, compared to Eulerian finite volume solutions of an (approximately) equivalent set of moment equations. The new approach is, by design, compatible with existing computational fluid dynamics codes that are used for multidimensional modelling of in-cylinder thermal fluids processes. This work broadens the accessibility of PDF methods for practical turbulent combustion systems.

scholarly journals Estimating survival probability using the terrestrial extinction history for the search for extraterrestrial life

2020 ◽  
Author(s):  
Kohji Tsumura
Keyword(s):  
Probability Density Function ◽  
Probability Density ◽  
Survival Probability ◽  
Normal Function ◽  
Extraterrestrial Life ◽  
New Approach ◽  
Random Multiplicative Process ◽  
Log Normal ◽  
Life On Earth ◽  
Fitted Function

Several exoplanets have been discovered to date, and the next step is the search for extraterrestrial life. However, it is difficult to estimate the number of life-bearing exoplanets because our only template is based on life on Earth. In this paper, a new approach is introduced to estimate the probability that life on Earth has survived from birth to the present based on its terrestrial extinction history. A histogram of the extinction intensity during the Phanerozoic Eon is modeled effectively with a log-normal function, supporting the idea that terrestrial extinction is a random multiplicative process. Assuming that the fitted function is a probability density function of extinction intensity per unit time, the estimated survival probability of life on Earth is ~0.15 from the beginning of life to the present. This value can be a constraint on fi in the Drake equation, which contributes to estimating the number of life-bearing exoplanets.

scholarly journals Seismic fragility curves based on the probability density evolution method

2017 ◽  
Vol 39 (2) ◽  
pp. 177-189
Author(s):  
Thuat-Cong Dang ◽  
Thien-Phu Le ◽  
Pascal Ray
Keyword(s):  
Probability Density ◽  
Seismic Vulnerability ◽  
Fragility Curves ◽  
Fragility Curve ◽  
Seismic Fragility ◽  
Cumulative Probability ◽  
Density Evolution ◽  
Probability Density Evolution Method ◽  
Log Normal ◽  
Probability Density Evolution

A seismic fragility curve that shows the probability of failure of a structure in function of a seismic intensity, for example peak ground acceleration (PGA), is a powerful tool for the evaluation of the seismic vulnerability of the structures in nuclear engineering and civil engineering. The common assumption of existing approaches is that the fragility curve is a cumulative probability log-normal function. In this paper, we propose a new technique for construction of seismic fragility curves by numerical simulation using the Probability Density Evolution Method (PDEM). From the joint probability density function between structural response and random variables of a system and/or excitations, seismic fragility curves can be derived without the log-normal assumption. The validation of the proposed technique is performed on two numerical examples.

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