Automaton partition logic versus quantum logic

The propositional system of a general class of discrete deterministic systems is formally characterized. We find that any finite prime orthomodular lattice allowing two-valued states can be represented by an automaton logic.     

Motzkin numbers out of Random Domino Automaton

Motzkin numbers are derived from a special case of Random Domino Automaton – recently proposed a slowly driven system being a stochastic toy model of earthquakes. It is also a generalisation of 1D Drossel–Schwabl forest-fire model. A solution of the set of equations describing stationary state of Random Domino Automaton in inverse-power case is presented. A link with Motzkin numbers allows to present explicit form of asymptotic behaviour of the automaton.     

A Modified Sensitive Driving Cellular Automaton Model

A modified cellular automaton model for traffic flow on highway is proposed with a novel concept about the variable security gap. The concept is first introduced into the original Nagel-Schreckenberg model, which is called the non-sensitive driving cellular automaton model. And then it is incorporated with a sensitive driving NaSch model, in which the randomization brake is arranged before the deterministic deceleration. A parameter related to the variable security gap is determined through simulation. Comparison of the simulation results indicates that the variable security gap has different influence on the two models. The fundamental diagram obtained by simulation with the modified sensitive driving NaSch model shows that the maximum flow are in good agreement with the observed data, indicating that the presented model is more reasonable and realistic.     

A Cellular Automaton Model for Two-Lane Traffic

We present some long time limit properties of a cellular automaton that models traffic of cars on a (infinite) two-lane road. This model, called TL184, is a natural generalization of the cellular automaton classified as 184 by Wolfram (to be abbreviated by CA184) and studied before as a model for one-lane traffic. TL184 models cars' motions on each lane by particles that interact via the CA184 rules, and cars' lane changes by a possibility for particles to flip from one CA184 to another. We calculate the infinite-time limit of the particle current in TL184, starting from a translation invariant measure, and use this result to show how the possibility of lane changes may enhance the current of cars in TL184 compared to that in a corresponding model of two non-interacting one-lane roads. We provide examples which demonstrate that even though the rules that regulate lane changes are completely symmetric, the system does not evolve to an equipartition of cars among both lanes from a given initially asymmetric distribution; moreover, the asymptotic car velocities and currents may be different on different lanes. We also show that, for a particular class of initial distributions, the asymptotic car density on a lane may be a non-monotonic function of the initial car density on this lane. Finally, we derive the current-density relation for an extended continuous-time version of TL184 with asymmetric lane-changing rules.     

Exact Solution of a Cellular Automaton for Traffic

We present an exact solution of a probabilistic cellular automaton for traffic with open boundary conditions, e.g., cars can enter and leave a part of a highway with certain probabilities. The model studied is the asymmetric exclusion process (ASEP) with simultaneous updating of all sites. It is equivalent to a special case (v _max=1) of the Nagel–Schreckenberg model for highway traffic, which has found many applications in real-time traffic simulations. The simultaneous updating induces additional strong short-range correlations compared to other updating schemes. The stationary state is written in terms of a matrix product solution. The corresponding algebra, which expresses a system-size recursion relation for the weights of the configurations, is quartic, in contrast to previous cases, in which the algebra is quadratic. We derive the phase diagram and compute various properties such as density profiles, two-point functions, and the fluctuations in the number of particles (cars) in the system. The current and the density profiles can be mapped onto the ASEP with other time-discrete updating procedures. Through use of this mapping, our results also give new results for these models.     

心肌组织机械形变的元胞自动机模拟

采用Greenberg-Hastings元胞自动机模型研究机械形变对心肌组织中螺旋波动力学行为的影响.数值模拟表明：对于规则网格下的稳定螺旋波,在生理性机械形变作用下,螺旋波发生漫游但不破碎;在病理性机械形变作用下,螺旋波会发生持续漫游、漫游后消失和破碎进入螺旋波湍流态三种变化.通过对比发现机械形变的振幅变化率对螺旋波的影响较大,而机械形变的角频率对螺旋波的影响较小.结合数值模拟,对心前区受到猛烈撞击会出现心颤致死及耐力运动员在发生心动过速后比一般人员更容易恢复正常进行解释.     

Cellular Automaton Simulation of Evacuation Process in Story

Computer simulations on the evacuation process in a story are launched with cellular automaton in this article. The story is composed of five rooms and one corridor. Influence of various parameters on the evacuation process is investigated. It shows that the width of the door of rooms has little influence but the width of the corridor and the maximum velocity of the pedestrian have great influence on the time for evacuation. The relation between evacuation time and the width of corridor is found as tc ∝ W^-0.84. It is also found that appropriate shape of the room is helpful to evacuation.     

Conservative logic

Conservative logic is a comprehensive model of computation which explicitly reflects a number of fundamental principles of physics, such as the reversibility of the dynamical laws and the conservation of certainadditive quantities (among which energy plays a distinguished role). Because it more closely mirrors physics than traditional models of computation, conservative logic is in a better position to provide indications concerning the realization of high-performance computing systems, i.e., of systems that make very efficient use of the computing resources actually offered by nature. In particular, conservative logic shows that it is ideally possible to build sequential circuits with zero internal power dissipation. After establishing a general framework, we discuss two specific models of computation. The first uses binary variables and is the conservative-logic counterpart of switching theory; this model proves that universal computing capabilities are compatible with the reversibility and conservation constraints. The second model, which is a refinement of the first, constitutes a substantial breakthrough in establishing a correspondence between computation and physics. In fact, this model is based on elastic collisions of identical balls, and thus is formally identical with the atomic model that underlies the (classical) kinetic theory of perfect gases. Quite literally, the functional behavior of a general-purpose digital computer can be reproduced by a perfect gas placed in a suitably shaped container and given appropriate initial conditions.This research was supported by the Defense Advanced Research Projects Agency and was monitored by the Office of Naval Research under Contract No. N000 14-75-C-0661.     

A Realistic Cellular Automaton Model for Synchronized Traffic Flow

A cellular automaton model is proposed to consider the anticipation effect in drivers＇ behavior. It is shown that the anticipation effect can be one of the origins of synchronized traffic flow. With anticipation effect, the congested traffic flow simulated by the model exhibits the features of synchronized flow. The spatiotemporal patterns induced by an on-ramp are also consistent with the three-phase traffic theory. Since the origin of synchronized flow is still controversial, our work can shed some light on the mechanism of synchronized flow.     

Cellular Automaton Simulations for Target Waves in Excitable Media

Using the Greenberg-Hasting cellular automata model, we study the properties of target waves in excitable media under the no-flux boundary conditions. For the system has only one excited state, the computer simulation and analysis lead to the conclusions that, the number of refractory states does not influence the wave-front speed; the wave- front speed decreases as the excitation threshold increases and increases as the neighbor radius increases; the period of target waves is equal to the number of cell states; the excitation condition for target waves is that the wave-front speed must be bigger than half of the neighbor radius.     

A Wave Automaton for Wave Propagation in Inhomogeneous Anisotropic Media

This paper presents an extension built on a hexagonal grid of the wave automaton, which was introduced in past few years for describing wave propagation in inhomogeneous media. This new method is capable of computing wave propagation in 2D anisotropic media without the need for introducing interpolating schemes. After a comparison of isotropic single scattering with analytical results using Mie theory, the method is used to compute the field scattered by one anisotropic particle for various orientations of its principal axes. Scattering by a collection of anisotropic particles is also presented.     

On quantum logic

The status and justification of quantum logic are reviewed. On the basis of several independent arguments it is concluded that it cannot be a logic in the philosophical sense of a general theory concerning the structure of valid inferences. Taken as a calculus for combining quantum mechanical propositions, it leaves a number of significant aspects of quantum physics unaccounted for. It is shown, moreover, that quantum logic, far from being more general than Boolean logic, forms a subset of a slight and natural extension of Boolean logic, a subset which corresponds to incomplete statements. The philosophical background of this unsatisfactory state of affairs is briefly explored.     

Coherent quantum logic

The von Neumann quantum logic lacks two basic symmetries of classical logic, that between sets and classes, and that between lower and higher order predicates. Similarly, the structural parallel between the set algebra and linear algebra of Grassmann and Peano was left incomplete by them in two respects. In this work a linear algebra is constructed that completes this correspondence and is interpreted as a new quantum logic that restores these invariances, and as a quantum set theory. It applies to experiments with coherent quantum phase relations between the quantum and the apparatus. The quantum set theory is applied to model a Lorentz-invariant quantum time-space complex.     

Unified quantum logic

Unified quantum logic based on unified operations of implication is formulated as an axiomatic calculus. Soundness and completeness are demonstrated using standard algebraic techniques. An embedding of quantum logic into a new modal system is carried out and discussed.On leave of absence from Department of Mathematics, University of Zagreb, Pot. Pret. 165, YU-41001 Zagreb, Yugoslavia.     

Optical logic redux

Twenty years ago IBM physicist Robert Keyes published a paper entitled “Optical Logic—in the light of computer technology.” It caused an instant furor in the fledgling optical logic community. Now, 20 years after that devastating critique, the field of optical logic has grown enormously. There are literally thousands of papers. Many of them are collected in a bibliography given here. Was Keyes’ critique wrong? Have opticists simply ignored what Keyes pointed out? Have new developments made some of his remarks not quite so relevant? We argue here that

•

Keyes was and still is mostly correct, but that may change in a few years

•

Many researchers have indeed simply ignored what he said

•

New developments in both optical logic and its applications open niches for optical logic that Keyes did not (and probably could not) anticipate

•

New and anticipated developments in electronics may increase the role for optics

     

Quantum logic revisited

An adequate conjunction-implication pair is given for complete orthomodular lattices. The resulting conjunction is noncommutative in nature. We use the well-known lattice of closed subspaces of a Hilbert space, to give physical meaning to the given lattice operation.To the memory of Thomas A. Brody.