Space-time Diagrams Research Articles

Optimization berth allocation in container terminals: A Pyomo and Google Colab approach

Efficient berth allocation profoundly influences container terminal operations, affecting vessel waiting and turnaround times, and overall performance. This study presents a mixed-integer linear programming (MILP) model addressing the Berth Allocation Problem (BAP) in a Malaysian container port. By incorporating the Pyomo optimization library and CBC (Coin-or Branch and Cut) solver in Google Colab, optimal berth allocations are determined, minimizing vessel turnaround times. Visualized in a Space-Time diagram, the results highlight efficient allocation strategies. Despite limitations, the study optimally resolved three instances, achieving a remarkable 38.54% reduction in overall vessel turnaround time compared to FCFS (First-Come-First-Serve) allocation. By prioritizing port turnaround time, the optimization substantially reduced berthing and departure delays, aligning with UNCTAD's call for enhanced port efficiency and accelerated decarbonization efforts.

The 4-Dimensional Spacetime World Line Image Representation and the Law of Existence of Objects Inferred from it

MINKOWSKI defined the four-dimensional spacetime model (x, y, z, t) used to represent world-point and world in [1]. The spacetime light cone is an intuitive diagram, compacted one space component and replaced it by time axis, thus the spacetime light cone was based on (x, y, t). In such a way, although it made the visual expression is possible, but also the spacetime light cone exposed shortages as follows • The spacetime light cone has limited expressive ability • The relationship between two or more world lines or events cannot be expressed • Can't express different world lines correctly • Most images of spacetime light cones are wrong and no use • The image of spacetime light cone is not intuitive and is obscure in application. Because of this, we designed the 4-dimensional Spacetime World Line image representation. This new 4-dimensional Spacetime diagram presents the complete 3 space dimensions and 1 time dimension. It overcomes the weakness of spacetime light cone, gives clear and precise visual expression of the world line, is able to display multi-world lines in one figure, can clearly present the interface and development process of each of the world line, and display the interaction among them. From the 4-dimensional spacetime diagram, we deducted and proved the Law of Existence of Object, which is as such: From its birth, through its past, to the present, and into the future, an object only exists at the "present" moment.

Comparative study of multidirectional pedestrian flows: Insights and dynamics

This study investigates multidirectional pedestrian flow by examining walking characteristics and behavioral factors impacting pedestrian dynamics. Parameters such as mean walking velocities, distance covered, and time taken by pedestrians were analyzed. Contrary to the expected inverse relationship between velocity and density, our findings revealed an increase in mean velocities in certain scenarios, attributed to conditions where the pedestrian density had not reached its maximum possible level and unpredicted pedestrian behaviors. Comparative analysis revealed that both Pakistani and Chinese pedestrians walk at nearly similar speeds. For instance, Pakistani pedestrians maintain a mean velocity of 1.36 ± 0.42 m/s at a density of 0.48 ped/m², while Chinese pedestrians maintain 1.27 ± 0.23 m/s at a density of 0.41 ped/m². Behavioral characteristics such as aggressive behavior, crowd avoidance, and waiting behavior were identified, with aggressive pedestrians exhibiting higher velocities than those avoiding crowds. A space-time diagram was utilized to categorize pedestrian flow types and behaviors, demonstrating increased stopping times with higher pedestrian numbers. Cultural factors, including side preferences, were analyzed using a binomial test, which returned a p-value of 0.968, indicating no significant preference for right-hand movement among Pakistani participants. These insights enhance the understanding of pedestrian dynamics and the influence of cultural norms on movement efficiency.

Training Teachers For New Ways Of Understanding Physics Teaching From Its Mathematization

Using mathematics in physics teaching often becomes an obstacle to learning. About this problem, we study possibilities of training future teachers for new understandings about the relationship between physics and mathematics. Our main frame of reference is a research sequence developed in the Teaching and Learning of Physics research group. Data arose from participant observation in the “Didactics of Physics” course in an initial teacher training program. It was qualitative research of case study type, with 20 students finishing their training process. We focused on addressing the "mathematization of physics for teaching" in three phases by developing ways to enrich classroom interaction using experimental resources, technologies, and literature. The three phases were the criteria for planning and executing the course. 1) Phenomenological approach; 2) Physical systems observation and; 3) Conceptual modeling. Results show how students substantially changed the way of creating explanations in physics to the point of being able to work on topics that they did not understand at the beginning, such as Minkowski diagrams, quantum entanglement, and the concept of entropy. We found evidence of real possibilities to get out of the traditional way of presenting mathematics in physics, understanding the mathematization as a natural and mental process to see nature.

Green Wave Control Model Simultaneously Considering Passenger Cars and Buses in Closed Road Networks

Existing green wave control methods for passenger cars and buses mainly focus on maximizing bandwidths at the arterial level. There is little research on green wave control for both at the closed road network level, which makes it difficult to improve the efficiency of the entire area. To address this, a green wave control model that considers both passenger cars and buses in closed road networks is presented in this paper. The objective function of the model is to maximize the sum of the weighted bandwidths of passenger cars and buses on each segment of the road network. The relationships between car green bands, bus green bands, offsets, phase sequences, red time, green time, etc. are analyzed on the level of arterials and road networks, respectively, using time–space diagrams. Based on these analyses, the key constraints of the model are constructed accordingly. In addition, 0/1 variables and a sufficiently large positive number M are introduced to relax some of the constraints to ensure that the presented model has feasible solutions. The results of the numerical example demonstrate that compared with the fixed phase sequence schemes 1, 2, and 3, the total weighted bandwidth generated by the presented model increased by 9.5%, 16.4%, and 17%, respectively. Compared with the model without constraint relaxation, the presented model can still find a global, optimal solution when the common cycle time is fixed, while the model without constraint relaxation has no feasible solution.

Development and assessment of trajectory-based arterial through percent arrivals on red for arterial signal coordination performance evaluation

Efficient traffic signal system management plays a pivotal role in reducing traffic congestion and improving traffic mobility on urban roads. The applications of the Automated Traffic Signal Performance Measures (ATSPM) revolutionize the way of proactively managing and evaluating traffic signal systems through a suite of performance measures. The Percent Arrivals on Red (PAoR) is one of the commonly used progression performance measures in the ATSPM to characterize vehicle arrivals at the intersection. However, the accuracy of PAoR to assess arterial signal coordination is restricted by configuration limitations of advance detectors and remains to be further explored. To address this problem, this research proposes an easy-to-use trajectory-based performance measure, Arterial Through Percent Arrivals on Red (ATPAoR), for arterial signal coordination performance evaluation and presents the general procedures to calculate ATPAoR from connected vehicle data. A case study is carried out to implement the proposed ATPAoR and investigate the relationship between the ATPAoR and the PAoR. It is found that the combination of the time–space diagram (TSD) and arterial through-vehicle trajectories is effective in the actual arterial signal coordination performance visualization, ATPAoR result interpretation, and potential timing improvement recommendations. The PAoR is found to be greater than the ATPAoR in undersaturated conditions, and the PAoR above 60% is recommended to identify poor arterial signal coordination design. The historical TSD can be utilized to verify the accuracy of the PAoR to evaluate the actual arterial signal coordination when vehicle trajectory data is unavailable.

A Lagrangian approach for variable speed limit implementation in C-ITS framework

With the development of Cooperative-Intelligent Transport System (C-ITS) technologies, new strategies based on embedded technologies have emerged to manage road networks. This paper focuses on adapting to this connectivity context a Variable Speed Limit (VSL) system to detect shockwaves and anticipate their propagation based on the kinematic wave theory to dampen them. We provide an alternative framework to adapt the VSL strategy, well-suited for Eulerian approaches, into a Lagrangian context. While the Eulerian approach is based on Loop Detector (LD) and macroscopic traffic indicators (e.g. flow, density), our Lagrangian approach relies on Road Side Units (RSUs) that record the GPS traces shared by Connected Vehicles (CVs). Based on the combination of CV trajectories, Fundamental and Space-Time Diagrams theory, shockwave estimation and prediction processes directly operate on congestion waves, which release the estimation issue for traffic density. The simulation-based analysis reveals that the performance of the Lagrangian approach is comparable to the Eulerian configurations.

Simulation limitations of affine cellular automata

Cellular automata are a famous model of computation, yet it is still a challenging task to assess the computational capacity of a given automaton; especially when it comes to showing negative results. In this paper, we focus on studying this problem via the notion of CA intrinsic simulation. We say that automaton A is simulated by B if each space-time diagram of A can be, after suitable transformations, reproduced by B.We study affine automata – i.e., automata whose local rules are affine mappings of vector spaces. This broad class contains the well-studied cases of linear automata. The main result of this paper shows that (almost) every automaton affine over a finite field Fp can only simulate affine automata over Fp. We discuss how this general result implies, and widely surpasses, limitations of linear and additive automata previously proved in the literature.We provide a formalization of the simulation notions into algebraic language and discuss how this opens a new path to showing negative results about the computational power of cellular automata using deeper algebraic theorems.

Time-Delay following Model for Connected and Automated Vehicles with Collision Conflicts and Forced Deceleration

The connected and automated car-following model can provide a model reference for the queue control algorithm of connected and automated driving and has become a hot research topic in the field of connected vehicles and intelligent transportation. A queue of fast-moving vehicles on urban roads can cause traffic congestion when forced to slow down and, in serious cases, can cause rear-impact accidents. Therefore, this paper introduces information on the time delay of information reception and processing, a collision risk quantification factor reflecting the speed characteristics of the front vehicle, and the speed limit and proposes an improved intelligent driver collision quantification model that considers drastic changes in the speed of the front vehicle. Additionally, the model parameters are calibrated using real vehicle data from urban roads combined with an improved salp swarm algorithm. Finally, the evolution rule of disturbance in the traffic flow under different states is analyzed using a time-space diagram, and the DIDM-CSCL model is compared with the classical IDM. The results show that the improved IDM can better describe the following behavior at the microscopic level, which provides a basis for research related to connected and automated driving.

Special relativity at Czech schools: a half-century comparison

In this contribution, we present the results of one bachelor and one master theses both devoted to the teaching of special relativity at an upper-secondary or intro-university level in the Czech Republic. We compare the test results of the grammar-school students in the school years 1976/1977 and 2021/2022, which are close to average and very similar in both cases, so the level of understanding has not changed in the meantime. We also present a set of interactive spacetime diagrams used in the preparation of future physics teachers within our relativity course.

Observational characteristics of oscillations and waves in and around sunspots. Difficulties in observing and interpreting

This paper summarizes the body of work that we have done over the years on the oscillation processes in sunspots, including their umbra, penumbra, and close vicinity. The study analyzes a number of aspects that impede adequate determining of some characteristics of propagating oscillations and lead to misinterpretation. Using running penumbral waves as an example, we show that their horizontal propagation with decreasing frequency is delusive. The effect is due to different oscillations propagating along magnetic field lines with gradually increasing inclination. This also applies to the three-minute oscillations in the sunspot umbral chromosphere. The change in the inclination of the strips in the half-tone space-time diagrams, which are employed to determine the oscillation propagation velocities along coronal loops, is caused by the projection effect as opposed to real changes in the velocity. We propose to use flare modulation of the natural oscillations of the medium to eliminate the uncertainties that arise while measuring the phase differences between signals of the same parameters, which is employed for estimating wave propagation velocities in the solar atmosphere.

Наблюдательные характеристики колебательно-волновых процессов в пятне и его окрестностях. Сложности наблюдений и интерпретации

This paper summarizes the body of work that we have done over the years on the oscillation processes in sunspots, including their umbra, penumbra, and close vicinity. The study analyzes a number of aspects that impede adequate determining of some characteristics of propagating oscillations and lead to misinterpretation. Using running penumbral waves as an example, we show that their horizontal propagation with decreasing frequency is delusive. The effect is due to different oscillations propagating along magnetic field lines with gradually increasing inclination. This also applies to the three-minute oscillations in the sunspot umbral chromosphere. The change in the inclination of the strips in the half-tone space-time diagrams, which are employed to determine the oscillation propagation velocities along coronal loops, is caused by the projection effect as opposed to real changes in the velocity. We propose to use flare modulation of the natural oscillations of the medium to eliminate the uncertainties that arise while measuring the phase differences between signals of the same parameters, which is employed for estimating wave propagation velocities in the solar atmosphere.

Airborne Ouzo: Evaporation-induced emulsification and phase separation dynamics of ternary droplets in acoustic levitation

We experimentally investigated the evaporation dynamics of acoustically levitated Ouzo droplets (a mixture of ethanol, water, and anise oil). Acoustic levitation has gained significant attention in various fields owing to its potential to create a lab-in-a-drop. Although evaporation is a key process in nature and industry, many studies have focused on single and binary components, and ternary droplets in acoustic levitation have rarely been experimentally investigated. In this study, the evaporation-induced spontaneous emulsification (the Ouzo effect) and phase separation process at 40–90 vol. % ethanol were visualized. We estimated the concentration change by evaporation of each component in the levitated ternary droplets based on an evaporation model to determine the experimental results. Our experimental results revealed four distinct stages of evaporation in levitated Ouzo droplets: (1) preferential evaporation of the volatile component (ethanol), (2) spontaneous emulsification (myriad micro-oil droplets generation), (3) phase separation forming a core–shell droplet, and (4) water evaporation completion resulting in the remaining oil droplets. Finally, we analyzed the emulsification process using a spacetime diagram. These findings suggest that acoustic levitation is suitable for physicochemical manipulation in mid-air.

A Simple Quantum Picture of the Relativistic Doppler Effect

The relativistic Doppler effect comes from the fact that observers in different inertial reference frames experience space and time differently, while the speed of light always remains the same. Consequently, a wave packet of light exhibits different frequencies, wavelengths, and amplitudes. In this paper, we present a local approach to the relativistic Doppler effect based on relativity, spatial and time translational symmetries, and energy conservation. Afterwards, we investigate the implications of the relativistic Doppler effect for the quantum state transformations of wave packets of light and show that a local photon is a local photon at the same point in the spacetime diagram in all inertial frames.

Traffic light optimization with low penetration rate vehicle trajectory data

Traffic light optimization is known to be a cost-effective method for reducing congestion and energy consumption in urban areas without changing physical road infrastructure. However, due to the high installation and maintenance costs of vehicle detectors, most intersections are controlled by fixed-time traffic signals that are not regularly optimized. To alleviate traffic congestion at intersections, we present a large-scale traffic signal re-timing system that uses a small percentage of vehicle trajectories as the only input without reliance on any detectors. We develop the probabilistic time-space diagram, which establishes the connection between a stochastic point-queue model and vehicle trajectories under the proposed Newellian coordinates. This model enables us to reconstruct the recurrent spatial-temporal traffic state by aggregating sufficient historical data. Optimization algorithms are then developed to update traffic signal parameters for intersections with optimality gaps. A real-world citywide test of the system was conducted in Birmingham, Michigan, and demonstrated that it decreased the delay and number of stops at signalized intersections by up to 20% and 30%, respectively. This system provides a scalable, sustainable, and efficient solution to traffic light optimization and can potentially be applied to every fixed-time signalized intersection in the world.

Time delay interferometry combination with zero-response

In space-based gravitational wave detection, gravitational wave signals are detected by measuring the Doppler frequency shift of laser exchange between three satellites. Although the laser is pre-stabilized, the laser phase noise is significantly higher than the gravitational wave signal, approximately 7–8 orders of magnitude higher. To reduce the otherwise-overwhelming laser phase noise, the time delay interferometry (TDI) technique is employed by properly time-shifting and linearly combining raw data. Different TDI combinations have various abilities in suppressing laser phase noise, and the response function of gravitational wave signal as well as the power spectral density of noise floor (including test mass acceleration noise and optical path noise) are also different. In this work, we present a unique class of TDI combinations, denoted as [ZX]116,[ZX]216,[ZX]316,[ZX]416, and [ZX]516, which exhibit a distinct geometric space–time diagrams composed of Michelson interferometers as the fundamental constituents. Specifically, when the detector arm lengths are assumed to be equal, these combinations yield response functions and noise power spectral densities of zero. To evaluate the detection performance of these combinations, we investigate their response functions and noise power spectral densities when the detector arm lengths are unequal, and furthermore, derive the analytical expressions for their sensitivity functions. Through our analysis, we have discovered some intriguing results. When the detector arm lengths are unequal, both the response functions and noise spectral densities of these combinations are correlated with the difference in arm lengths L3−L2. However, the sensitivity functions of these TDI combinations remain unaffected by the specific values of the arm length difference, and are consistent with the sensitivity functions of widely-used TDI combinations. For instance, the sensitivity function of [ZX]116 combination is the same as that of the Michelson combination, while the sensitivity functions of [ZX]216 and [ZX]416 combinations match with that of the Sagnac combination. Furthermore, the [ZX]316 and [ZX]516 combinations share the same sensitivity function as the fully symmetric Sagnac combination, enabling the identification of instrument noise and stochastic gravitational wave backgrounds. The discovery of this class of combinations provides support for the diversity of data processing.

ALIGNMENT OF FINGERING PATTERN INDUCED BY AN INTERFACIAL NEUTRALIZATION REACTION

In this paper, we numerically study buoyancy-driven chemoconvective instabilities in a vertically oriented Hele-Shaw cell. At the beginning, the cavity is filled with a homogeneous aqueous solution of a strong inorganic alkali, and this system is statically stable. We assume that the upper boundary is free, and a fixed value of the concentration of a strong inorganic acid is set there. After bringing the reactants into contact, density stratification quickly becomes unstable due to a neutralization reaction, resulting in density fingering. The mathematical model includes the effect of producing a new amount of solvent (water). We show that this effect is a reason for the sudden alignment of salt fingers that we previously observed in experiments. In this work, we carry out a formal parametric study of the system with a change in the dimensionless parameter responsible for the intensity of water production. One can interpret this variation as a sequential consideration of substances from the homologous series of alkalis. We show that there exists a critical value of the parameter, crossing which one can observe a spontaneous transition from an irregular fingering pattern to cellular chemoconvection. The latter looks like a system of fingers tightly pressed against each other with tips aligned along a horizontal line. The lower boundary of the vortices uniformly moves down. We found that instead of the usual coarsening of the structure, one observes an increase in the aspect ratio of vortices. We investigate the dynamics of the lower boundary of the fingering pattern and changes in the pattern wavelength. Complex rearrangements of the reaction front, which include the processes of plume creation and coalescence, are illustrated using space-time diagrams.

From rectangle to parallelogram: an area-weighted method to make time-space diagrams incorporate traffic waves

From rectangle to parallelogram: an area-weighted method to make time-space diagrams incorporate traffic waves

Geogebra supporting materials for introductory physics university courses

In this contribution, we present a set of Geogebra activities used in several introductory courses on Classical mechanics, Special relativity, Introductory course to cosmology and within the courses for non-physics majors (Physics for chemists, Physics for biologists). Examples include various oscillations, curvilinear coordinates, solutions of equations of motion, basic types of Minkowski spacetime diagrams and the effective potential for the dynamic of basic cosmological models. All the activities include basic interactivity and the possibility to play with selected parameters. They are used within the classrooms and shared with the students via links in the Moodle LMS platform together with other supporting materials.

One-Dimensional Cellular Automaton Transitions and Integral Value Transformations Representing Deoxyribonucleic Acid Sequence Evolutions

The cellular automaton (CA) and an integral value transformation (IVT) evolving in discrete time steps are two mathematical models that are well established. Theoretically, it can be suggested that a CA possesses the capacity to produce varieties of evolutionary patterns. However, computing a CA in higher dimensions or computing a nonlinear CA may be complex. In such cases, an IVT can be conveniently used. This paper presents the relation between the transition functions of a one-dimensional CA and an IVT. It also highlights the algebraic structures on the basis of binary operations for a set of transition functions of a one-dimensional CA and for a set of IVTs. The suitability of using an IVT over a CA is discussed. Also, we present the evolutionary models of two deoxyribonucleic acid (DNA) sequences through IVTs and their spacetime diagrams. This can eventually bring out some characteristic features of the evolutionary sequences.