Space-time Diagrams Research Articles

Modelling of Unsteady Transition in Low-Pressure Turbine Blade Flows with Two Dynamic Intermittency Equations

A transition model for describing wake-induced transition is presented based on the SST turbulence model by Menter and two dynamic equations for intermittency: one for near-wall intermittency and one for free-stream intermittency. In the Navier-Stokes equations, the total intermittency factor, which is the sum of the two, multiplies the turbulent viscosity computed by the turbulence model. The quality of the transition model is illustrated on the T106A test cascade for two Reynolds numbers, using experimental results by Stieger and Hodson for transition mainly due to kinematic wake impact on a separation bubble. The quality of the model is also revealed on the T106D test cascade using experimental results from Hilgenfeld, Stadtmuller and Fottner for wake turbulence induced transition. The test cases differ in pitch to chord ratio, Reynolds number and inlet free-stream turbulence intensity, causing different transition mechanisms. The unsteady results are presented in space-time diagrams of shape factor and wall shear stress on the suction side. The results show the capability of the model to capture the physics of unsteady transition in separated state. Inevitable shortcomings are revealed as well.

On the Role of Multiple Interactions in Remote Aftershock Triggering: The Landers and the Hector Mine Case Studies

The observed seismicity rate increase after large earthquakes in sites that are located several source lengths away from the mainshock centroid poses a major problem. This is because the static stress change induced by a mainshock in that region seems to be insignificant, and the dynamic stress changes can only en- hance the seismicity during the passage of the seismic waves but not at later times. In quest for a physically viable triggering mechanism for delayed aftershocks in remote sites, we examine earthquake activities in remote sites that were triggered by two California earthquakes, the magnitude 7.1 Hector Mine earthquake and the mag- nitude 7.3 Landers earthquake. We introduce a new method for quantifying the de- gree to which the triggering effect of each aftershock is locally more important than the triggering effect of the mainshock. We apply this method to the Landers and the Hector Mine remote aftershock sequences. We show that multiple stress transfers from early aftershocks to later aftershocks played an important role in the enhance- ment of both the Landers and the Hector Mine aftershock activities in remote sites. We present a time-space diagram of the Hector Mine remote aftershock sequence in the Imperial Valley, which shows that this sequence is made up of several subse- quences and that the onset of activity migrated southward.

Relativistic Flight Mechanics and Space Travel

Relativistic Flight Mechanics and Space Travel is about the fascinating prospect of future human space travel. Its purpose is to demonstrate that such ventures may not be as difficult as one might believe and are certainly not impossible. The foundations for relativistic flight mechanics are provided in a clear and instructive manner by using well established principles which are used to explore space flight possibilities within and beyond our galaxy. The main substance of the book begins with a background review of Einstein's Special Theory of Relativity as it pertains to relativistic flight mechanics and space travel. The book explores the dynamics and kinematics of relativistic space flight from the point of view of the astronauts in the spacecraft and compares these with those observed by earth's scientists and engineers-differences that are quite surprising. A quasi historical treatment leads quite naturally into the central subject areas of the book where attention is focused n various issues not ordinarily covered by such treatment. To accomplish this, numerous simple thought experiments are used to bring rather complicated subject matter down to a level easily understood by most readers with an engineering or science background. The primary subjects regarding photon rocketry and space travel are covered in some depth and include a flight plan together with numerous calculations represented in graphical form. A geometric treatment of relativistic effects by using Minkowski diagrams is included for completeness. The book concludes with brief discussions of other prospective, even exotic, transport systems for relativistic space travel. A glossary and simple end-of-chapter problems with answers enhance the learning process.

Study of complex behavior in a time-delayed van der Pol’s electromagnetic system (Ⅱ)——Pattern dynamics in spatiotemporal chaos

Based on a simple infinite dimensional electromagnetic system consisting of a linear lossless transmission line in combination with a nonlinear boundary condition, the local map of backward voltage wave is established by using the traveling wave theory. The numerical simulation results show rich spatiotemporal nonlinear phenomena in the voltage wave on the lossless transmission line. The pattern dynamics in spatiotemporal chaos of the voltage wave on the lossless transmission line are qualitatively analyzed by depicting space-amplitude plot and space-time diagram. A good model with solution is established to study and understand the spatiotemporal chaos.

Graphical aids for visualising the space-time coordinates of events created by light signals emitted by moving sources

Relativistic space-time diagrams are presented, displaying in true values the space-time coordinates of events created by light signals emitted by moving sources, as detected from inertial reference frames in relative motion. The diagrams are used in order to solve the problem of the rays and mirrors in the Michelson-Morley experiment.

Interactions, Dynamics and Self-assembly of Magnetic Holes

ABSTRACTNonmagnetic microspheres dispersed in a ferrofluid are denoted magnetic holes. When the spheres are confined to a monolayer between two plane, parallel plates and subjected to AC magnetic fields, they show a variety of dynamical behaviors and assemblages. The magnetic interactions between the particles and their dynamical behavior are influenced by the boundaries and the degree of confinement. We have derived analytical results for the pair-wise competing interactions, and these compare favorably with experimental results.It is also possible to characterize the self-assembly and dynamics of the spheres by the theory of braids. It involves classifying different ways of tracing curves in space. The essentially two-dimensional motion of a sphere can be represented as a curve in a three-dimensional space-time diagram, and so several spheres in motion produce a set of braided curves. The dynamical modes can then be described in terms of braid-words. We also present a few other examples on how this system can be used to study dynamical processes.

MODELING FIXED-BLOCK RAILWAY SIGNALING SYSTEM USING CELLULAR AUTOMATA MODEL

In this paper, we propose a new cellular automata model to simulate the railway traffic. The proposed model is based on deterministic NaSch traffic model. The signaling system adopted in this work is the three-aspect fixed-block signaling system. In order to obtain insight into the characteristic behavior of the railway signaling system, we analyze the space-time diagram of traffic flow and the trajectory of train movement etc. The simulation results demonstrate that the proposed CA model can be successfully used for the simulations of railway signaling system. Some complex phenomena observed in railway system can be reproduced.

Flat Space Gravitation

A new description of gravitational motion will be proposed. It is part of the proper time formulation of physics as presented on the IARD 2000 conference. According to this formulation the proper time of an object is taken as its fourth coordinate. As a consequence, one obtains a circular space–time diagram where distances are measured with the Euclidean metric. The relativistic factor turns out to be of simple goniometric origin. It further follows that the Lagrangian for gravitational dynamics does not require an interpretation in terms of curvature of space–time. The flat space model for gravitational dynamics leads to the correct predictions for the bending of light, the perihelion shift of Mercury and gravitational red-shift. The new theory is free of singularities. More important, the new formulation of gravitational dynamics restores the validity of the principle of addition of potentials. One therefore can find solutions for static gravitational configurations for which it is difficult to find the solution of the corresponding Einstein equations. The method will be illustrated by means of the orbital precession for non-spherical stellar mass distributions. In case of the bipole mass distribution the agreement with the predictions of the general theory of relativity is very striking. Nevertheless, the new model is far more simple.

Black hole evaporation: a paradigm

A paradigm describing black hole evaporation in non-perturbative quantum gravity is developed by combining two sets of detailed results: (i) resolution of the Schwarzschild singularity using quantum geometry methods and (ii) time evolution of black holes in the trapping and dynamical horizon frameworks. Quantum geometry effects introduce a major modification in the traditional spacetime diagram of black hole evaporation, providing a possible mechanism for recovery of information that is classically lost in the process of black hole formation. The paradigm is developed directly in the Lorentzian regime and necessary conditions for its viability are discussed. If these conditions are met, much of the tension between expectations based on spacetime geometry and structure of quantum theory would be resolved.

Ultrashort pulse propagation in uniform and nonuniform waveguide long-period gratings

We conduct a detailed theoretical analysis of ultrashort pulse propagation through waveguide long-period grating (LPG) structures operating in the linear regime. We first consider the case of uniform LPGs, and we also investigate the effect of the typical grating nonuniformities, e.g., grating profile apodization, grating period chirping, and discrete phase shifts, on the spectral and temporal behavior of LPG structures. The two interacting modes are analyzed separately, and advanced representation tools, namely, space-wavelength and space-time diagrams (where space refers to the longitudinal grating dimension), are used to provide a deeper insight into the physics that determines the pulse evolution dynamics through the grating structures under analysis. In addition to its intrinsic physical interest, our study reveals the strong potential of LPG-based devices for optical pulse reshaping operations in the subpicosecond regime.

Cellular automaton model for railway traffic

Based on the deterministic NaSch model, we propose a new cellular automation (CA) model to simulate the railway traffic. Using the proposed CA model, we analyze the space-time diagram of traffic flow and the trajectory of train movement, etc. Our aim is to investigate the characteristic behavior of railway traffic flow. A number of simulation results demonstrate that the proposed model can be successfully used for the simulation of railway traffic. Some complex phenomena can be reproduced, such as the go-and-stop wave and the complex behavior of train movement.

Surface potential mapping of an argon lamp during electrical breakdown

In this paper, we present measurements related to the early stages of electrical breakdown occurring in a low-pressure argon straight discharge tube. A capacitive probe was used to retrieve the evolution of the lamp electrostatic potential over time and space. The potential and calculated electric field, displayed in space-time diagrams, show that a region of strong potential gradient propagates from the cathode toward the anode and then backward. This is followed by a homogenization of the electric field in the inter-electrode space.

Kinetics of Localized Plasticity Macrodomains at the Prefracture Stage in Metals

The behavior of localized plasticity macrodomains is experimentally studied at the final stage of the plastic flow in going to necking and ductile fracture in fcc, bcc, and hcp materials. General features of the localization process at the stage of prefracture are found. They are a constant velocity of domains and their tendency to consistently move toward the focus of a bundle of straight lines in space-time diagrams. A correlation between the type of fracture and the kinetics of localized plasticity domains is established.

Resonant Cycles in Traffic Signal Control

The potential benefits of using resonant cycle times in traffic signal control on an arterial are investigated. Resonant cycles are cycle lengths that result in good arterial progression over a range of traffic flows. The notion of resonant cycle times contrasts with the prevalent adaptive control practice of setting the arterial cycle length in proportion to flow levels at the most congested intersection on the arterial. This research was motivated by the development of appropriate adaptive algorithms for closed-loop system control in the FHWA ACS-Lite project. Simulation experiments with TRANSYT-7F for a four-intersection arterial and additional time–space diagrams demonstrate the characteristics of resonant cycle times and the substantial performance benefits that they may offer. In addition, a systematic method was developed to identify appropriate resonant cycle times and fine-tune a schedule for a time-of-day signal timing strategy.

Resonant Cycles in Traffic Signal Control

The potential benefits of using resonant cycle times in traffic signal control on an arterial are investigated. Resonant cycles are cycle lengths that result in good arterial progression over a range of traffic flows. The notion of resonant cycle times contrasts with the prevalent adaptive control practice of setting the arterial cycle length in proportion to flow levels at the most congested intersection on the arterial. This research was motivated by the development of appropriate adaptive algorithms for closed-loop system control in the FHWA ACS-Lite project. Simulation experiments with TRANSYT-7F for a four-intersection arterial and additional time-space diagrams demonstrate the characteristics of resonant cycle times and the substantial performance benefits that they may offer. In addition, a systematic method was developed to identify appropriate resonant cycle times and fine-tune a schedule for a time-of-day signal timing strategy.

From Einstein's 1905 postulates to the geometry of flat space-time

Minkowski diagrams in 1+1 dimensional flat space-time are given a strictly geometric derivation, directly from two gedanken experiments incorporating the principle of the constancy of the velocity of light and the principle of (special) relativity. Rectangles of photon trajectories play a central role in determining the simultaneity convention and in establishing the invariance of the interval.

Analyse spatio-temporelle de jets axisymétriques d'air et d'hélium

The effects of strong density variations on the dynamics of instabilities which develop in axisymmetric jets of pure air or pure helium are studied in the near field. By using LDV measurements associated with fast visualization techniques, space–time diagrams are built in order to show the evolution of the structures along the jets according to their Reynolds number and their density. In particular, the global character of the helium jet instabilities is highlighted. To cite this article: S. Boujemaa et al., C. R. Mecanique 332 (2004).

Railroad simulation using OpenTrack

OpenTrack is a user-friendly railroad network simulation program developed at the Swiss Federal Institute of Technology's Institute for Transportation Planning and Systems (ETH IVT). It is a microscopic model that simulates rail system operations based on user defined train, infrastructure, and timetable databases. OpenTrack functions as a railroad laboratory, by, for example, allowing users to define incidents and take infrastructure out of service to evaluate alternative scenarios. The program uses a mixed discrete/continuous simulation process that calculates both the continuous solution of train motion equations and the discrete processes of signal box states and delay distributions. It generates a wide variety of data that can be easily presented in many formats including graphs (e.g. time-space diagrams), tables, and images. OpenTrack's main uses have been to 'evaluate and test infrastructure plans and operating schedules to optimize network and timetable design. It can be run on several different computer platforms and incorporates the benefits of an object oriented programming language with a common data interface structure.

Mr. Tompkins in Java: Interactive Lorentz transformations

This paper describes a simple applet for illustrating Lorentz transformations. The user specifies stationary and moving objects and light pulses, and sees animations of two reference frames. Even with minimal graphics (the objects are colored dots and the light flashes are expanding circles), such animations can make the concepts of redshift, length contraction, time dilation, and non-simultaneity more intuitive than traditional spacetime diagrams.

Experimental Study of a Buoyant Particle Dispersion in Pipe Flow

An experimental investigation of a solid–liquid dispersion pipe flow was conducted using a pulsed ultrasonic Doppler velocimeter. The solid phase was composed of buoyant particles dispersed in water. This particular two-phase flow was used to mimic the behaviour of ice–water flow. Four diagnostics were used to study the complex nature of the two-phase flow mixtures: mean velocity profiles, space-time diagrams, probability density functions (PDF) and cumulative probability distribution functions (CPDF) of velocities. The results allow detection of the different flow patterns with moving bed, sliding and saltation regimes. Visualizations of the flow supplement the velocity measurements.