Space-time Diagrams Research Articles

ARTIFICIAL MICRO-WORLDS PART III: A TAXONOMY OF SELF-REPRODUCING 2D CA SPECIES

2D k-totalistic CA are life-like Artificial Micro-Worlds (AMWs), which contain a large variety of self-reproducing species. In this paper we present a gallery of these systems, with simple and complex behavior. Firstly, we present two simple self-reproducer species, with a linear behavior and then two self-reproducer species with a rhombic development. A curious double-strand self-reproducer completes this first part of the self-reproducing species taxonomy. We present then other interesting new species: their reproductive phenomena are more complex, resulting in space-time diagrams of great variety.

A study of mixing in coherent vortices using braiding factors

This paper studies the use of braiding fluid particles to quantify the amount of mixing within a fluid flow. We analyze the pros and cons of braid methods by considering the motion of three or more fluid particles in a coherent vortex structure. The relative motions of the particles, as seen in a space–time diagram, produce a braid pattern, which is correlated with mixing and measured by the braiding factor.The flow we consider is a Gaussian vortex within a rotating strain field that generates cat's eyes in the vortex. We also consider a modified version of this strain field that contains a resonance frequency effect that produces multiple sets of cat's eyes at different radii. As the thickness of the cat's eyes increases, they interact with one another and produce complex Lagrangian motion in the flow that increases the braiding of particles, hence implying more mixing within the vortex.It is found that calculating the braiding factor using only three fluid particles gives useful information about the flow, but only if all three particles lie in the same region of the flow, i.e. this gives good local information. We find that we only require one of the three particles to trace a chaotic path to give an exponentially growing braiding factor. i.e. a non-zero ‘braiding exponent’. A modified braiding exponent is also introduced which removes the spurious effects caused by the rotation of the fluid.This analysis is extended to a more global approach by using multiple fluid particles that span larger regions of the fluid. Using these global results, we compare the braiding within a viscously spreading Gaussian vortex in the above strain fields, where the flow is determined both kinematically and dynamically. We show that the dynamic feedback of the strain field onto the flow field reduces the overall amount of braiding of the fluid particles.

Analysing collisions using Minkowski diagrams in momentum space

Momentum space and Minkowski diagrams are powerful tools for interpreting and analysing relativistic collisions in one or two spatial dimensions. All relevant quantities that characterize a collision, including the mass, velocity, momentum and energy of the interacting particles, both before and after collision, can be directly seen from a single Minkowski diagram. Such diagrams can also be useful for analysing the differences between Newtonian and relativistic mechanics. As an interesting example, a simple derivation of the Compton wavelength shift formula, based on the geometrical properties of such momentum space diagrams, is also presented.

A numerical investigation of high-Reynolds-number constant-volume non-Boussinesq density currents in deep ambient

The time-dependent behaviour of non-Boussinesq high-Reynolds-number density currents, released from a lock of height h0 and length x0 into a deep ambient and spreading over horizontal flat boundaries, is considered. We use two-dimensional Navier–Stokes simulations to cover: (i) a wide range of current-to-ambient density ratios, (ii) a range of length-to-height aspect ratios of the initial release within the lock (termed the lock aspect ratio λ = x0/h0) and (iii) the different phases of spreading, from the initial acceleration phase to the self-similar regimes. The Navier–Stokes results are compared with predictions of a one-layer shallow-water model. In particular, we derive novel insights on the influence of the lock aspect ratio (λ) on the shape and motion of the current. It is shown that for lock aspect ratios below a critical value (λcrit), the dynamics of the current is significantly influenced by λ. We conjecture that λcrit depends on two characteristic time scales, namely the time it takes for the receding perturbation created at the lock upon release to reflect back to the front, and the time of formation of the current head. A comparison of the two with space–time diagrams obtained from the Navier–Stokes simulations supports this conjecture. The non-Boussinesq effect is observed to be significant. While the critical lock aspect ratio (λcrit) is of order 1 for Boussinesq currents, its value decreases for heavy currents and increases significantly (up to about 20) for light currents. We present a simple analytical model which captures this trend, as well as the observation that for a light current the speed of propagation is proportional to λ1/4 when λ < λcrit.

Neutrino Oscillations: Entanglement, Energy-Momentum Conservation and QFT

We consider several subtle aspects of the theory of neutrino oscillations which have been under discussion recently. We show that the $S$-matrix formalism of quantum field theory can adequately describe neutrino oscillations if correct physics conditions are imposed. This includes space-time localization of the neutrino production and detection processes. Space-time diagrams are introduced, which characterize this localization and illustrate the coherence issues of neutrino oscillations. We discuss two approaches to calculations of the transition amplitudes, which allow different physics interpretations: (i) using configuration-space wave packets for the involved particles, which leads to approximate conservation laws for their mean energies and momenta; (ii) calculating first a plane-wave amplitude of the process, which exhibits exact energy-momentum conservation, and then convoluting it with the momentum-space wave packets of the involved particles. We show that these two approaches are equivalent. Kinematic entanglement (which is invoked to ensure exact energy-momentum conservation in neutrino oscillations) and subsequent disentanglement of the neutrinos and recoiling states are in fact irrelevant when the wave packets are considered. We demonstrate that the contribution of the recoil particle to the oscillation phase is negligible provided that the coherence conditions for neutrino production and detection are satisfied. Unlike in the previous situation, the phases of both neutrinos from $Z^0$ decay are important, leading to a realization of the Einstein-Podolsky-Rosen paradox.

Bulking I: An abstract theory of bulking

This paper is the first part of a series of two papers dealing with bulking: a quasi-order on cellular automata comparing space–time diagrams up to some rescaling. Bulking is a generalization of grouping taking into account universality phenomena, giving rise to a maximal equivalence class. In the present paper, we discuss the proper components of grouping and study the most general extensions. We identify the most general space–time transforms and give an axiomatization of bulking quasi-order. Finally, we study some properties of intrinsically universal cellular automata obtained by comparing grouping to bulking.

Bulking II: Classifications of cellular automata

This paper is the second part of a series of two papers dealing with bulking: a way to define quasi-order on cellular automata by comparing space-time diagrams up to rescaling. In the present paper, we introduce three notions of simulation between cellular automata and study the quasi-order structures induced by these simulation relations on the whole set of cellular automata. Various aspects of these quasi-orders are considered (induced equivalence relations, maximum elements, induced orders, etc.) providing several formal tools allowing to classify cellular automata.

Acoustic–convective mode conversion in an aerofoil cascade

When an acoustic wave impinges on an aerofoil cascade, a convective vorticity mode is generated giving rise to transverse velocity perturbations. This mode conversion process is investigated to explain the flow dynamics observed when swirlers are submitted to incident acoustic disturbances. The phenomenon is first studied in the case of a two-dimensional aerofoil cascade using a model derived from an actuator disk theory. The model is simplified to deal with low-Mach-number flows. The velocity field on the downstream side of the cascade features two components, an axial perturbation associated with the transmitted acoustic wave and a transverse disturbance corresponding to the vorticity wave generated at the cascade trailing edge. The model provides the amplitude of both components and defines their phase shift. Numerical simulations are carried out in a second stage to validate this model in the case of a cascade operating at a low Reynolds number Rec = 2700 based on the chord length. Space–time diagrams of velocity perturbations deduced from these simulations are used to retrieve the two types of modes. Experiments are then carried out in the case of an axial swirler placed in a cylindrical duct and submitted to plane acoustic waves emitted on the upstream side of the swirler. The amplitude and phase of the two velocity components measured in the axial and azimuthal directions are found to be in good agreement with theoretical estimates and with numerical calculations. This analysis is motivated by combustion dynamics observed in flames stabilized by aerodynamic swirlers in continuous combustors.

Dynamic response of metals under high-intensity pulsed ion beam irradiation for surface modification

A piezoelectric transducer based on lead–zirconte–titanate (PZT) piezoelectric ceramic thin plate was applied to characterize the stress waves in titanium targets under high-intensity pulsed ion beam (HIPIB) irradiation at a peak accelerating voltage of 350 kV and an ion current density up to 400 A/cm 2 with pulse duration of about 150 ns. The magnitude of recorded stress wave signals was increased along with the irradiation intensity, presenting a slow growth with a value below 100 V in the range of 200–300 A/cm 2, and then a rapid increase of about four times up to 400 A/cm 2. The measured stress waves were explained by space–time diagram analysis. The generation and propagation of the stress wave can be attributed to the coupled thermal–dynamic effects during HIPIB irradiation onto metallic targets, where the thermal shock due to ultra-fast heating/cooling process and the recoil impulse due to ablation process have a combined contribution to the induced stress waves, dependent on the irradiation intensity. It is indicated that a fast attenuation of stress wave proceeded during its propagation from the irradiated surface to the target/PZT interface. The large amount of energy delivered by the stress wave effectively converted and dissipated into plastic deformation and/or defects formation in target materials. The dynamic response of metallic materials under HIPIB irradiation accounts for the effective surface modification of metals and alloys into a depth well beyond the ion range.

Variability of Sub-Canopy Flow, Temperature, and Horizontal Advection in Moderately Complex Terrain

We examine the space–time structure of the wind and temperature fields, as well as that of the resulting spatial temperature gradients and horizontal advection of sensible heat, in the sub-canopy of a forest with a dense overstorey in moderately complex terrain. Data were collected from a sensor network consisting of ten stations and subject to orthogonal decomposition using the multiresolution basis set and stochastic analyses including two-point correlations, dimensional structure functions, and various other bulk measures for space and time variability. Despite some similarities, fundamental differences were found in the space–time structure of the motions dominating the variability of the sub-canopy wind and temperature fields. The dominating motions occupy similar spatial, but different temporal, scales. A conceptual space–time diagram was constructed based on the stochastic analysis that includes the important end members of the spatial and temporal scales of the observed motions of both variables. Short-lived and small-scale motions govern the variability of the wind, while the diurnal temperature oscillation driven by the surface radiative transfer is the main determinant of the variability in the temperature signal, which occupies much larger time scales. This scale mismatch renders Taylor’s hypothesis for sub-canopy flow invalid and aggravates the computation of meaningful estimates of horizontal advective fluxes without dense spatial information. It may further explain the ambiguous and inconclusive results reported in numerous energy and mass balance and advection studies evaluating the hypothesis that accounting for budget components other than the change in storage term and the vertical turbulent flux improves the budget closure when turbulent diffusion is suppressed in plant canopies. Estimates of spatial temperature gradients and advective fluxes were sensitive to the network geometry and the spatial interpolation method. The assumption of linear spatial temperature gradients was not supported by the results, and leads to increased spatial and temporal variability of inferred spatial gradients and advection estimates. A method is proposed to estimate the appropriate minimum network size of wind and temperature sensors suitable for an evaluation of energy and mass balances by reducing spatial and temporal variability of the spatially sampled signals, which was estimated to be on the order of 200 m at the study site.

A Self-tuning Signal Control Algorithm for Isolated Intersections Based on Time-space Diagrams

In this study, a self-tuning signal control algorithm is developed for isolated intersections. Traffic dynamics at signalized intersections are represented on time-space diagrams using the shockwave theory and information from detectors installed upstream of intersections. Splits are incrementally adjusted so that the delay per cycle is gradually diminished. Cycles are modified to have an efficient use of the provided green times without causing the residual queues. Unlike most algorithms, the proposed method uses occupancy information and can manage traffic even when queues extend beyond detector locations. Simulation experiments on a four-phase intersection with different demand scenarios are performed to demonstrate efficiency of the developed algorithm. Hypothesis tests are conducted to statistically verify the efficiency comparison between the proposed method and the Webster formula. It is found that in case of fixed demand, the proposed method can optimize splits and cycle lengths with no worse performance measures than the optimal fixed-time signal settings. For the variable demand case, the result indicates that the algorithm can adjust splits and cycle lengths in response to the change of demand and provides better performance measures than the Webster formula. The proposed algorithm has demonstrated itself to be a potential split and cycle optimization for an adaptive signal control system.

A Self-tuning Signal Control Algorithm for Isolated Intersections Based on Time-space Diagrams

A Self-tuning Signal Control Algorithm for Isolated Intersections Based on Time-space Diagrams

Selfsimilarity, Simulation and Spacetime Symmetries

We study intrinsic simulations between cellular automata and introduce a new necessary condition for a CA to simulate another one. Although expressed for general CA, this condition is targeted towards surjective CA and especially linear ones. Following the approach introduced by the first author in an earlier paper, we develop proof techniques to tell whether some linear CA can simulate another linear CA. Besides rigorous proofs, the necessary condition for the simulation to occur can be heuristically checked via simple observations of typical space-time diagrams generated from finite configurations. As an illustration, we give an example of linear reversible CA which cannot simulate the identity and which is 'time-asymmetric', i.e. which can neither simulate its own inverse, nor the mirror of its own inverse.

THE EFFECT OF THE HETEROGENEITY ON THE TRAFFIC FLOW BEHAVIOR

We propose a traffic flow model which takes into account the disorder in the length and the maximal speed of cars. Using cellular automaton model in parallel dynamics we have studied the behavior of traffic flow, especially the condition of formation (active phase) and the dissociation (absorbing phase) of platoons. It is found that the transition from active to absorbing phase depend on the length of the slow vehicles L2. Indeed, the transition is discontinuous for L2 = 1 and continuous when L2 > 1. In the later case, the critical exponent is calculated near the transition density, and the space-time diagram shows the presence of the two phases. Furthermore, we have found that the fundamental diagram exhibit a plateau which depend on the size of the system.

The Asynchronous Bounded-Cycle model

This paper shows how synchrony conditions can be added to the purely asynchronous model in a way that avoids any reference to message delays and computing step times, as well as system-wide constraints on execution patterns and network topology. Our Asynchronous Bounded-Cycle (ABC) model just bounds the ratio of the number of forward- and backward-oriented messages in certain (“relevant”) cycles in the space–time diagram of an asynchronous execution. We show that clock synchronization and lock-step rounds can be implemented and proved correct in the ABC model, even in the presence of Byzantine failures. Furthermore, we prove that any algorithm working correctly in the partially synchronous Θ-Model also works correctly in the ABC model. In our proof, we first apply a novel method for assigning certain message delays to asynchronous executions, which is based on a variant of Farkas’ theorem of linear inequalities and a non-standard cycle space of graphs. Using methods from point-set topology, we then prove that the existence of this delay assignment implies model indistinguishability for time-free safety and liveness properties. We also introduce several weaker variants of the ABC model, and relate our model to the existing partially synchronous system models, in particular, the classic models of Dwork, Lynch and Stockmayer and the query–response model by Mostefaoui, Mourgaya, and Raynal. Finally, we discuss some aspects of the ABC model’s applicability in real systems, in particular, in the context of VLSI Systems-on-Chip.

Dynamo generated field emergence through recurrent plasmoid ejections

AbstractMagnetic buoyancy is believed to drive the transport of magnetic flux tubes from the convection zone to the surface of the Sun. The magnetic fields form twisted loop-like structures in the solar atmosphere. In this paper we use helical forcing to produce a large-scale dynamo-generated magnetic field, which rises even without magnetic buoyancy. A two layer system is used as computational domain where the upper part represents the solar atmosphere. Here, the evolution of the magnetic field is solved with the stress–and–relax method. Below this region a magnetic field is produced by a helical forcing function in the momentum equation, which leads to dynamo action. We find twisted magnetic fields emerging frequently to the outer layer, forming arch-like structures. In addition, recurrent plasmoid ejections can be found by looking at space–time diagrams of the magnetic field. Recent simulations in spherical coordinates show similar results.

Low-Pressure Dynamical Glow Discharge With Electrolytic Cathode in the Form of Aqueous Solution of $\hbox{NaHCO}_{3}$

Video images of a low-pressure dc glow discharge with an electrolytic cathode in the form of aqueous solution of sodium bicarbonate NaHCO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sub> are presented in this paper. Various forms of the discharge are observed. One of the discharge forms-a dc glow discharge with a foam cathode-was recorded for the first time. A space-time diagram of the discharge is drawn.

A novel cellular automata based technique for visual multimedia content encryption

This paper proposes a new method for visual multimedia content encryption using Cellular Automata (CA). The encryption scheme is based on the application of an attribute of the CLF XOR filter, according to which the original content of a cellular neighborhood can be reconstructed following a predetermined number of repeated applications of the filter. The encryption is achieved using a key image of the same dimensions as the image being encrypted. This technique is accompanied by the one-time pad (OTP) encryption method, rendering the proposed method reasonably powerful, given the very large number of resultant potential security keys. The method presented here makes encryption possible in cases where there is more than one image with the use of just one key image. A further significant characteristic of the proposed method is that it demonstrates how techniques from the field of image retrieval can be used in the field of image encryption. The proposed method is further strengthened by the fact that the resulting encrypted image for a given key image is different each time. The encryption result depends on the structure of an artificial image produced by the superposition of four 1-D CA time–space diagrams as well as from a CA random number generator. A semi-blind source separation algorithm is used to decrypt the encrypted image. The result of the decryption is a lossless representation of the encrypted image. Simulation results demonstrate the effectiveness of the proposed encryption method. The proposed method is implemented in C# and is available online through the img(Rummager) application.

Improvement of Classical Algebraic Method of Signal Timing for Arterial Road Coordinate Control

AbstractFollowing the design principle of maximum green wave bandwidth and making use of the time-space diagram for arterial road coordinate control, many problems existed in classical algebraic method such as the determination of value range of ideal intersection distance, the calculation of green wave bandwidth, the selection of optimal intersection distance and the value of signal offsets were deeply analyzed through some practical examples. On the basis of detailed analysis, the value range of ideal intersection distance was determined by the allowable value range of common signal cycle, a new calculation method for green wave bandwidth was presented, and a new selection rule of optimal intersection distance was established. The examples effectively demonstrate that the improved classical algebraic method can make arterial road coordinate control system get green wave bandwidth as wide as possible and obtain optimal common signal cycle and green wave bandwidth more practically and accurately.

Optical and electrostatic potential investigations of electrical breakdown phenomena in a low-pressure gas discharge lamp

The ignition phase is a critical stage in the operation of gas discharge lamps where the neutral gas enclosed between the electrodes undergoes a transformation from the dielectric state to a conducting phase, eventually enabling the production of light. The phenomena occurring during this phase transition are not fully understood and the related experimental studies are often limited to local optical measurements in environments prone to influencing these transient phenomena. In this work unipolar ignition phenomena at sub-kilovolt levels are investigated in a 3 Torr argon discharge tube. The lamp is placed in a highly controlled environment so as to prevent any bias on the measurements. A fast intensified CCD camera and a specially designed novel electrostatic probe are used simultaneously so as to provide a broad array of measured and computed parameters which are displayed in space–time diagrams for cross comparisons. Experiments show that three distinct phases exist during successful ignitions: upon the application of voltage a first ionization wave starts from the active electrode and propagates in the neutral gas towards the opposite electrode. A local front of high axial E field strength is associated with this process and causes a local ionization to occur, leading to the electrostatic charging of the lamp. Next, a second wave propagates from the ground electrode back towards the active electrode with a higher velocity, and in this process leads to a partial discharging of the lamp. This return stroke draws a homogeneous plasma column which eventually bridges both electrodes at the end of the wave propagation. At this point both electrode sheaths are formed and the common features of a glow discharge are observed. The third phase is an increase in the light intensity of the plasma column until the lamp reaches a steady-state operation. Failed ignitions present only the first phase where the first wave starts its propagation but extinguishes in the lamp, leading to a charge memory effect. It is found that the full propagation of this first wave is a requirement for successful lamp ignition. Differences in the properties of the waves were observed depending on the voltage polarity, and it was estimated that a photoelectric effect at the wall is the most likely source of electrons for the ionization wave of positive polarity. Finally, a simple model of the first ionization wave is developed and used to analyse the fundamental differences between processes occurring at negative and at positive polarity. From this study three conditions are developed for the successful unipolar ignition of lamps and the relations between them are derived.