Space-time Diagrams Research Articles

Perturbation threshold and hysteresis associated with the transition to turbulence in sudden expansion pipe flow

The complex flow resulting from the laminar-turbulent transition in a sudden expansion pipe flow, with expansion ratio of 1:2, subjected to an inlet parabolic velocity profile and a vortex perturbation, is investigated by means of direct numerical simulations. It is shown that the threshold amplitude for disordered motion is described by a power law scaling, with -3 exponent, as a function of the subcritical Reynolds number. The instability originates from a region of intense shear rate, which results on the flow symmetry breakdown. Above the threshold, several unsteady states are identified using space-time diagrams of the centreline axial velocity fluctuation and their energy. In addition, the simulations show a small hysteresis transition mode due to the reestablishment of the recirculation region in the subcritical range of Reynolds numbers, which depends on: (i) The initial and final quasi-steady states, (ii) the observation time and (iii) the number of intermediate steps taken when increasing and decreasing the Reynolds number.

Learning the space-time phase diagram of bacterial swarm expansion

Coordinated dynamics of individual components in active matter are an essential aspect of life on all scales. Establishing a comprehensive, causal connection between intracellular, intercellular, and macroscopic behaviors has remained a major challenge due to limitations in data acquisition and analysis techniques suitable for multiscale dynamics. Here, we combine a high-throughput adaptive microscopy approach with machine learning, to identify key biological and physical mechanisms that determine distinct microscopic and macroscopic collective behavior phases which develop as Bacillus subtilis swarms expand over five orders of magnitude in space. Our experiments, continuum modeling, and particle-based simulations reveal that macroscopic swarm expansion is primarily driven by cellular growth kinetics, whereas the microscopic swarming motility phases are dominated by physical cell-cell interactions. These results provide a unified understanding of bacterial multiscale behavioral complexity in swarms.

Research for Urban Traffic Simulation Model of Cross-street Pedestrian Influence

To study the influence of cross-street pedestrian on the urban traffic flow, traffic characteristic of vehicle and pedestrian are investigated under horizontal interference conditions. With resetting the rules of vehicle operation behaviour such as deceleration, acceleration, lane change, etc, a new simulation model of two-lane urban traffic flow is established, which is also called cellular automata model. To simulate the traffic conditions of signal control road sections and non-signal control road sections and generate the space-time diagram, the softwares MATLAB and ORIGIN is used for acquiring numerical simulating results and relational graphs of the traffic flow parameters. Comparative analysis is carried on between traffic state with horizontal interference and traffic state without horizontal interference. Finally, simulation results show that pedestrian crossing street has less obvious impact on traffic flow in larger density (higher than 0.22), signal control and acceptable crossing gaps for pedestrian have certain influence on traffic flow and lane change of vehicle. The proposed simulation model is in better consistence with actual situation and has some practical and theoretical significance for traffic flow research.

Dynamic analysis of pedestrian movement in single-file experiment under limited visibility

In this paper, the movement properties of pedestrians under limited visibility are investigated by a group of single-file experiments. Three light transmissions (0.3%, 0.1% and 0.0%) are set and trajectories of individuals are extracted by using tracking algorithm. From the analysis of experimental video, typical behavior of following the boundary and frontal pedestrian are observed under poor visibility. Velocity distribution in different experiment runs conforms to Gaussian distribution. Two regimes are found in the headway–velocity relation and the time-space diagram reveals the evolution of pedestrian traffic with the decrease of visibility. Fundamental diagrams are obtained through the proposed measurement method and three regions can be found in the density-flow relation. The maximum specific flow under the light transmission of 0.3%, 0.1% and 0.0% is 1.3 s−1, 1.15 s−1 and 0.9 s−1 respectively. Finally log transformation for density and velocity is performed to study the elastic effect of density change on velocity change. It is found that pedestrians are more sensitive to the density change under good visibility. This study is helpful to understand pedestrian movement characteristics under different visibilities, which is of practical importance for pedestrian safety under emergency condition. Furthermore, the valuable data obtained from the experiment can be used for model validation and verification in the future.

Slicing conditions for axisymmetric gravitational collapse of Brill waves

In numerical relativity, spacetimes involving compact strongly gravitating objects are constructed as numerical solutions of Einstein’s equations. Success of such a process strongly depends on the availability of appropriate coordinates, which are typically constructed dynamically. A very robust coordinate choice is a so-called moving puncture gauge, commonly used for numerical simulations of black hole spacetimes. Nevertheless it is known to fail for evolving near-critical Brill wave data. We construct a new ‘quasi-maximal’ slicing condition and demonstrate that it exhibits better behavior for such data. This condition is based on the 1+log slicing with an additional source term derived from maximal slicing. It is relatively simple to implement in existing moving puncture codes and computationally inexpensive. We also illustrate the properties of constructed spacetimes based on gauge-independent quantities in compactified spacetime diagrams. These invariants are also used to show how created black holes settle down to a Schwarzschild black hole.

A Cooperative Co-Evolutionary Optimisation Model for Best-Fit Aircraft Sequence and Feasible Runway Configuration in a Multi-Runway Airport

A careful arrival and departure sequencing of aircraft can reduce the inter-arrival/departure time, thereby opening up opportunities for new landing and/or take-off slots, which may increase the runway throughput. This sequence when serviced with a suitable runway configuration may result in an optimal aircraft sequence with a runway configuration that can process the maximum number of aircraft within a given time interval. In this paper, we propose a Cooperative Co-evolutionary Genetic Algorithm (CCoGA) to find the combined solution of a best-fit sequence with a feasible runway configuration for a given traffic demand at an airport. The aircraft sequence and the runway configuration are modelled as individual species, which can cooperatively interact with each other. Therefore, we computationally evolve the best possible combination of aircraft sequence (arrival and departure) and the feasible runway configuration. The proposed CCoGA algorithm is evaluated for Chicago O’Hare International Airport runway layout and resulting configurations. Arrival and departure traffic demand is modelled through a Poisson distribution. Two different arrival/departure sequencing methods, i.e., constraint position shifting with one, two and N-position shifting and first come first serve, are modelled. Runway configuration and traffic sequence (arrivals and departure) are modelled as two species, which are evolved co-operatively, through the CCoGA algorithm, to achieve the optimal traffic sequencing with a feasible runway configuration. Time-space diagrams are presented for the best-evolved population of arrival-departure sequence and runway configuration to illustrate the possibility of using available departure slots between arrivals to maximize capacity. Arrival-departure capacity envelopes are then presented to illustrate the trade-off between the arrivals and departures, given a runway configuration for each sequencing method. Results demonstrate the high mutual dependence between arrival-departure sequence and the runway configuration, as well as its effect on overall runway capacity. The results also demonstrate the viability of using evolutionary computation-based methods for modelling and evaluating complex problems in the air transport domain.

Resurrecting the Lost Vehicle Trajectories of Treiterer and Myers with New Insights into a Controversial Hysteresis

The 1974 paper by Treiterer and Myers is a seminal work in traffic flow theory. This longevity is in part because of the impressive collection of manually extracted vehicle trajectories. To date, only a few studies have rivaled the scale of the empirical vehicle trajectory data used in Treiterer and Myers. Their data collection used high-speed aerial photography and manual data reduction to follow hundreds of vehicles. In spite of the Herculean collection effort, the trajectory data set was never released and has since been lost. Fortunately, the plots survive and the present work re-extracts the vehicle trajectory data from the time–space diagrams. The discussion places the value of the data in context and then uses the data to put an end to decades of misinterpretation that started with Treiterer himself. The central thesis of Treiterer and Myers generated considerable interest: a hysteresis whereby drivers exhibit different fundamental behavior depending on whether they are entering or exiting a disturbance. There has been extensive debate about the authors’ findings in the literature, but without the original data set any interpretation has required considerable speculation. With the resurrected trajectories, this work reexamines the vehicles underlying the hysteresis and finally quells the speculation. Rather than arising from car following behavior, it turns out that the enigmatic progression arose from a combination of lane change maneuvers and unremarkable transitions into or out of the congested regime. On publication, the re-extracted data from this paper will be released to the research community.

Playing Tag relativistically

The present paper summarizes in detail various relativistic effects related, some loosely, some closely, to the Dewan–Beran paradox. The aim of the paper is to deepen students’ understanding of the surprising properties of flat spacetime in a way that is enjoyable and easily accessible at the undergraduate level. The paper relies heavily on spacetime diagrams, a useful tool to visualize and understand relativistic phenomena.

The Influence of Accretion Disk Thickness on the Large-scale Magnetic Dynamo

Abstract The evolution of the magnetic field from the large-scale dynamo is considered a central feature of the accretion disk around a black hole. The resulting low-frequency oscillations introduced from the growth and decay of the field strength, along with the change in field orientation, play an integral role in the accretion disk behavior. Despite the importance of this process and how commonly it is invoked to explain variable features, it still remains poorly understood. We present a study of the dynamo using a suite of four global, high-resolution, MHD accretion disk simulations. We systematically vary the scale height ratio and find the large-scale dynamo fails to organize above a scale height ratio of h/r ≳ 0.2. Using spacetime diagrams of the azimuthal magnetic field, we show the large-scale dynamo is well ordered in the thinner accretion disk models, but fails to develop the characteristic “butterfly” pattern when the scale height ratio is increased, a feature which is also reflected in the power spectra. Additionally, we calculate the dynamo α-parameter and generate synthetic light curves. Using an emission proxy, we find the disks have markedly different characters as stochastic photometric fluctuations have a larger amplitude when the dynamo is unordered.

Towards the map of quantum gravity

In this paper we point out some possible links between different approaches to quantum gravity and theories of the Planck scale physics. In particular, connections between loop quantum gravity, causal dynamical triangulations, Hořava–Lifshitz gravity, asymptotic safety scenario, Quantum Graphity, deformations of relativistic symmetries and nonlinear phase space models are discussed. The main focus is on quantum deformations of the Hypersurface Deformations Algebra and Poincaré algebra, nonlinear structure of phase space, the running dimension of spacetime and nontrivial phase diagram of quantum gravity. We present an attempt to arrange the observed relations in the form of a graph, highlighting different aspects of quantum gravity. The analysis is performed in the spirit of a mind map, which represents the architectural approach to the studied theory, being a natural way to describe the properties of a complex system. We hope that the constructed graphs (maps) will turn out to be helpful in uncovering the global picture of quantum gravity as a particular complex system and serve as a useful guide for the researchers.

An extended continuum traffic model with the consideration of the optimal velocity difference

In this letter, we derived an extended continuum model from a car-following model with consideration of the optimal velocity difference called the relative optimal velocity via employing the transformation relation from microscopic variables to macroscopic ones. The stability condition of this continuum traffic model is obtained by performing linear stability analysis. Results show that the optimal velocity difference helps to improve the stability of traffic flow. We make use of the upwind finite difference scheme for simulation. The effects of the optimal velocity difference (the relative optimal velocity) and the velocity difference (the optimal velocity) on local clustering effect and instability are studied and compared each other, respectively. The spatiotemporal evolution patterns of traffic flow for the different initial density, strength of the optimal velocity difference and the velocity-difference are obtained. Their space–time diagrams reveal the local clustering effect induced by the instability of traffic flow and generate the stop&go traffic jams. Numerical simulation result indicates the unstable region is shrunken under the effect of the optimal velocity difference (the relative optimal velocity) and/or the velocity difference (the optimal velocity).

Identification and quantification of human microcirculatory leukocytes using handheld video microscopes at the bedside.

Leukocyte recruitment and adhesion to the endothelium are hallmarks of systemic inflammation that manifest in a wide range of diseases. At present, no method is available to directly measure leukocyte kinetics at the bedside. In this study, we validate a new method to identify and quantify microcirculatory leukocytes observed by handheld vital microscopy (HVM) using space-time diagram (STD) analysis. Video clips ( n = 59) containing one capillary-postcapillary venule unit where leukocytes could be observed emanating from a capillary into a venule in cardiac surgery patients ( n = 20) were included. STD analysis and manual counting were used to quantify the number of leukocytes (total, rolling, and nonrolling). Pearson's correlation and Bland-Altman analysis were used to determine agreement between the STDs and manual counting. For reproducibility, intra- and interobserver coefficients of variation (CVs) were assessed. Leukocyte (rolling and nonrolling) and red blood cell velocities were assessed. The STDs and manual counting procedures for the quantification of rolling leukocytes showed good agreement ( r = 0.8197, P < 0.0001), with a Bland-Altman analysis mean difference of -0.0 (-6.56; 6.56). The overall intraobserver CV for the STD method was 1.5%. The overall interobserver CVs for the STD and the manual method were 5.6% and 9.4%, respectively. The nonrolling velocity was significantly higher than the rolling velocity (812 ± 519 µm/s vs. 201 ± 149 µm/s, P = 0.001). STD results agreed with the manual counting procedure results, had a better reproducibility, and could assess the leukocyte velocity. STD analysis using bedside HVM imaging presented a new methodology for quantifying leukocyte kinetics and functions in the microcirculation. NEW & NOTEWORTHY In this study, we introduce space-time diagram analysis of sublingual microcirculation imaging using handheld vital microscopy to identify and quantify the presence and kinetics of human microcirculatory leukocytes. We validated the methodology by choosing anatomical units consisting of a capillary connected to a venule, which allowed precise identification of leukocytes.

Entanglement entropy with a time-dependent Hamiltonian

The time evolution of entanglement tracks how information propagates in interacting quantum systems. We study entanglement entropy in ${\mathrm{CFT}}_{2}$ with a time-dependent Hamiltonian. We perturb by operators with time-dependent source functions and use the replica trick to calculate higher-order corrections to entanglement entropy. At first order, we compute the correction due to a metric perturbation in ${\mathrm{AdS}}_{3}/{\mathrm{CFT}}_{2}$ and find agreement on both sides of the duality. Past first order, we find evidence of a universal structure of entanglement propagation to all orders. The central feature is that interactions entangle unentangled excitations. Entanglement propagates according to ``entanglement diagrams,'' proposed structures that are motivated by accessory spacetime diagrams for real-time perturbation theory. To illustrate the mechanisms involved, we compute higher-order corrections to free fermion entanglement entropy. We identify an unentangled operator, one which does not change the entanglement entropy to any order. Then, we introduce an interaction and find it changes entanglement entropy by entangling the unentangled excitations. The entanglement propagates in line with our conjecture. We compute several entanglement diagrams. We provide tools to simplify the computation of loop entanglement diagrams, which probe UV effects in entanglement propagation in CFT and holography.

A General Maximum Progression Model to Concurrently Synchronize Left-Turn and through Traffic Flows on an Arterial

In the existing bandwidth-based methods, through traffic flows are considered as the coordination objects and offered progression bands accordingly. However, at certain times or nodes in the road network, when the left-turn traffic flows have a higher priority than the through traffic flows, it would be inappropriate to still provide the progression bands to the through traffic flows; the left-turn traffic flows should instead be considered as the coordination objects to potentially achieve better control. Considering this, a general maximum progression model to concurrently synchronize left-turn and through traffic flows is established by using a time-space diagram. The general model can deal with all the patterns of the left-turn phases by introducing two new binary variables into the constraints; that is, these variables allow all the patterns of the left-turn phases to deal with a single formulation. By using the measures of effectiveness (average delay time, average vehicle stops, and average travel time) acquired by a traffic simulation software, VISSIM, the validity of the general model is verified. The results show that, compared with the MULTIBAND, the proposed general model can effectively reduce the delay time, vehicle stops, and travel time and, thus, achieve better traffic control.

An Improved Single-Lane Cellular Automaton Model considering Driver’s Radical Feature

Traffic flow models are of vital significance to study the traffic system and reproduce typical traffic phenomena. In the process of establishing traffic flow models, human factors need to be considered particularly to enhance the performance of the models. Accordingly, a series of car-following models and cellular automaton models were proposed based on comprehensive consideration of various driving behaviors. Based on the comfortable driving (CD) model, this paper innovatively proposed an improved cellular automaton model incorporating impaired driver’s radical feature (RF). The impaired driver’s radical feature was added to the model with respect to three aspects, that is, desired speed, car-following behavior, and braking behavior. Empirical data obtained from a highway segment was used to initialize impaired driver’s radical feature distribution and calibrate the proposed model. Then, numerical simulations validated that the proposed improved model can well reproduce the traffic phenomena, as shown by the fundamental diagram and space-time diagram. Also, in low-density state, it can be found that the RF model is superior to the CD model in simulating the speed difference characteristics, where the average speed difference of adjacent vehicles for RF model is more consistent with reality. The result also discussed the potential impact of impaired drivers on rear-end collisions. It should be noted that this study is an early stage work to evaluate the existence of impaired driving behavior.

On Mass, Spacetime Curvature, and Gravity

The frequently used analogy of a massive ball distorting an elastic sheet, which is used to illustrate why mass causes spacetime curvature and gravitational attraction, is criticized in this article. A different analogy that draws on the students’ previous knowledge of spacetime diagrams in special relativity is suggested.

Phase Optimization Procedure for Two-Way Synchronization of Fixed Traffic Signals on an Urban Passageway in Washington City (USA)

Traffic Congestion on major corridor consequent upon existing lacuna in signal control strategy is a major problem in Washington City. To change this trend this research is carried out to design the efficient phase optimization technique using developed phase plan. C G Road was identified as a troubled corridor during reconnaissance survey and as such, selected for study. Three intersection of the road having length of 805 m harvests maximum straight movers forward direction 2nd cycle delay of 110.5 sec while backward direction 2nd cycle right turner delay of 59.87 sec due to absence of signal coordination. To contend the situation applying phase optimization three phase plan A, A1 & A2 has been prepared and presented through time space diagram to solve two way coordination problem. Data on geometric features were collected by Field survey using Odometer as well as with Google Earth Software. Peak and off peak hour traffic volume data were collected using ultra high resolution full HD camera. Furthermore signal cycle timing, space mean speed, discharge head way were simultaneously collected by trained enumerator’s at all three intersections. Data extraction was carried out on projector screen using updated VLC media player. The geometric and traffic data collected were analyzed with Microsoft Excel. Constructed by developed method three different Phase Optimization Technique (POT) is tested on real traffic signal data of corridor in forward and backward direction using Time Space Diagram. With change of phase plan and phase sequence POT 1 is successful in minimizing combined delay of corridor up to 28.05% to 76.04 % for all 4 forward movements for analyzed two cycles. Further improvement in POT 2 is achieved by introducing 10 second offset at intersection B which reduces combined delay up to 32.52% to 98.6% in all 4 forward movements. Tracking average travel time, demand supply and prevailing signal cycle time POT 3 is applied with equal signal cycle length of 104 second at all 3 intersections. This method is capable to reduce right turner delay up to 21.91% to 49.57% while it produces unhindered movement with no delay for straight through traffic along corridor in both forward and backward direction.

The self-slowing behavioral mechanism of pedestrians under normal and emergency conditions

We study the similarities and differences between the headway-velocity relations under normal and emergency conditions to explore whether they can be described by a unified behavioral equation. We firstly performed a series of pedestrian experiments in three different scenes under normal and emergency conditions respectively to obtain the behavioral parameters of headway-velocity relations based on the visual hindrance field as well as the high precise trajectories of pedestrians. The strong similarities in the headway-velocity relations in both normal and emergency conditions suggest that a unified behavioral mechanism is at play in human-driven pedestrian traffic. This mechanism is essentially a safety-driven self-slowing behavior that pedestrians try to adopt a safe speed for a given spacing between them to avoid collisions and preserve their personal space. We notice that even in emergency escape situations, people still tend to slow down the speed and show defensive behavior when the headway approaches a critical value in order to decrease the collision level and protect the body from contact as much as possible. Moreover, the differences between normal and emergency conditions are also found in the experiments. Compared to normal condition, the free velocity of pedestrians is markedly higher while the minimum critical headway is much shorter in emergency situation. Especially, the proportionality constant, the reciprocal of which is safe response time, is higher under emergency condition. That means pedestrians will slow down the free speed to zero in a shorter safe response time in emergencies. A modified social force model is then proposed to incorporate this self-slowing behavioral mechanism, and different self-slowing behavioral parameters in the model under normal and emergency conditions both refer to the observed experimental data. Simulations with the same setup as the experiments were carried out for both normal and emergency conditions using the unified model with self-slowing, and the simulated spacetime diagrams as well as stop-and-go waves in circular movement under normal condition, the simulated evacuation efficiency in room evacuation under emergency condition and the simulated velocity profiles in corridor scene under normal and emergency conditions all demonstrate remarkable consistency with the experimental results.

Evaluation of Red Clearance Extension designs with Hardware-in-the-Loop simulation

Advances in signal controller software and hardware are introducing new safety-enhancing functions to the signal engineer’s toolbox. Hardware-in-the-Loop (HITL) simulation can evaluate alternative timing parameters, detection strategies, and intersection geometries in a safe and cost-effective manner. Red Clearance Extension (RCE) is one design alternative that can be evaluated by HITL simulation. RCE operates by predicting Red Light Running vehicles and dynamically increasing red clearance interval duration to reduce crash probability. In this study, HITL simulation was used to evaluate four alternative RCE detection strategies. Novel code was developed in R to visualize output in Enhanced Time-Space Diagrams (ETSDs). RLR vehicles triggered the highest rate of correct RCE events when the downstream detection alternative was used. However, the ETSDs showed that RCE events triggered by smart upstream speed-conditional detection alternatives at 125, 215, and 475 ft provided greater safety for vehicles with no significant increase to intersection delay incurred.

Assessment of endothelial cell function and physiological microcirculatory reserve by video microscopy using a topical acetylcholine and nitroglycerin challenge

BackgroundAssessment of the microcirculation is a promising target for the hemodynamic management of critically ill patients. However, just as the sole reliance on macrocirculatory parameters, single static parameters of the microcirculation may not represent a sufficient guide. Our hypothesis was that by serial topical application of acetylcholine (ACH) and nitroglycerin (NG), the sublingual microcirculation can be challenged to determine its endothelial cell-dependent and smooth muscle-dependent physiological reserve capacity.MethodsIn 41 healthy subjects, sublingual capillary microscopy was performed before and after topical application of ACH and NG. Total vessel density (TVD) was assessed in parallel using manual computer-assisted image analysis as well as a fully automated analysis pathway utilizing a newly developed computer algorithm. Flow velocity was assessed using space-time diagrams of the venules as well as the algorithm-based calculation of an average perfused speed indicator (APSI).ResultsNo change in all measured parameters was detected after sublingual topical application of ACH. Sublingual topical application of NG however led to an increase in TVD, space-time diagram-derived venular flow velocity and APSI. No difference was detected in heart rate, blood pressure, and cardiac output as measured by echocardiography, as well as in plasma nitric oxide metabolite content before and after the topical application of ACH and NG.ConclusionsIn healthy subjects, the sublingual microcirculatory physiological reserve can be assessed non-invasively by topical application of nitroglycerin without affecting systemic circulation.