In this paper, we investigate non-uniform elementary cellular automata (i.e., one-dimensional cellular automata whose cells can use different Wolfram rules to update their states) in the context of ...number conservation. As a result, we obtain an exhaustive characterization of such number-conserving cellular automata on all finite grids both with periodic and null boundary conditions. The characterization obtained allows, inter alia, to enumerate all number-conserving non-uniform elementary cellular automata, in particular those that are reversible. Surprisingly, the numbers obtained are closely related to the Fibonacci sequence.
This paper concerns two-dimensional cellular automata on a triangular grid that preserve the sum of the states of all the cells. To study such cellular automata, we adapt the idea of the ...split-and-perturb decomposition of a number-conserving local rule, developed first for square grids, to the setting of triangular grids. As a result, we obtain a new mathematical tool that allows, for example, to enumerate all so-called k-ary (i.e., binary, ternary, quaternary, quinary, etc.) number-conserving cellular automata on a triangular grid, regardless of the value of k.
We introduce a novel method to study the reversibility of d-dimensional number-conserving multi-state cellular automata with the von Neumann neighborhood. We apply this method to ternary such ...cellular automata, for which, up to now, nothing was known about their reversibility. It turns out that they are all trivial: the only reversible such cellular automata are shifts that are intrinsically 1-dimensional.
A
bstract
We extend previous studies of the conformal 0+1d kinetic non-equilibrium attractor in relaxation time approximation by enforcing number conservation through the introduction of a dynamical ...fugacity (chemical potential). We derive two coupled integral equations for the effective temperature and fugacity which are then solved numerically to obtain the exact solution. The resulting solutions exhibit convergence to a unique non- equilibrium attractor when the scaled moments of the distribution function are plotted as a function of the rescaled time
w
¯
=
τ
/
τ
eq
.
This occurs even though the system is out of chemical equilibrium at late times. In addition, compared to the case where number conservation was not imposed, we find that the moments converge to their respective attractors more quickly, particularly for moments with
m
= 0. Finally, we compare the resulting attractor moments with predictions from different hydrodynamic frameworks.
We present a novel method to study two-dimensional rotation-symmetric number-conserving multi-state cellular automata with the von Neumann neighborhood with radius one. This method enables a succinct ...and easy enumeration in all cases examined so far in literature, i.e., cellular automata with at most five states. Moreover, it allows to find all such cellular automata with six and seven states, while so far, even enumerating six-state rules was beyond the reach of computing machines. Such enumeration allows us to revisit some unresolved questions in the field. Furthermore, we give some rough estimates of the asymptotic growth of the number of such cellular automata with n states, as n tends to infinity. The results are obtained for finite square grids with periodic boundary conditions, but they are also valid in the case of the infinite square grid.
Discrete dynamical systems such as cellular automata are vastly used as models of complex physical phenomena. For this reason, the problem of reversibility of such systems is very important and ...recurrently taken up by researchers. Unfortunately, the study of reversibility is remarkably hard, even in the case of one-dimensional cellular automata. We propose a novel method that really supports the investigation of the reversibility of number-conserving cellular automata, i.e, cellular automata that preserve the sum of the states of all the cells upon every update. This method allows to enumerate all so-called k-ary (binary, ternary, quaternary, quinary, etc.) number-conserving cellular automata that are reversible and this for a fairly wide range of values of the parameter k.
•Algorithms for enumeration of 1D reversible number-conserving cellular automata.•Use cases for 1D reversible number-conserving CA with five, six, and seven states.•Comprehensive description of dynamics for such CA with five states is presented.
This paper concerns d-dimensional cellular automata with the von Neumann neighborhood that conserve the sum of the states of all their cells. These automata, called number-conserving or ...density-conserving cellular automata, are of particular interest to mathematicians, computer scientists and physicists, as they can serve as models of physical phenomena obeying some conservation law. We propose a new approach to study such cellular automata that works in any dimension d and for any set of states Q. Essentially, the local rule of a cellular automaton is decomposed into two parts: a split function and a perturbation. This decomposition is unique and, moreover, the set of all possible split functions has a very simple structure, while the set of all perturbations forms a linear space and is therefore very easy to describe in terms of a basis. We show how this approach allows to find all number-conserving cellular automata in many cases of d and Q. In particular, we find all three-dimensional number-conserving CAs with three states, which until now was beyond the capabilities of computers.
•A novel approach to study number conservation of cellular automata is proposed.•We prove that any number-conserving local rule is a sum of two well-defined units.•This decomposition is unique and holds for any dimension and any state set.•The effectiveness of the decomposition theorem is illustrated via several examples.
Multiple hard and semi-hard parton scatterings in high-energy p+A collisions involve multi-parton correlation inside the projectile in both momentum and flavor which will lead to modification of the ...final hadron spectra relative to that in p+p collisions. Such modification of the final hadron transverse momentum spectra in p+A collisions is studied within HIJING 2.1 Monte Carlo model which includes nuclear shadowing of the initial parton distributions and transverse momentum broadening. Multi-parton flavor and momentum correlation inside the projectile are incorporated through flavor and momentum conservation which are shown to modify the flavor content and momentum spectra of final partons and most importantly lead to suppression of large pT hadron spectra in p+A collisions at both RHIC and LHC energies.
PDF
