Phenomenology of nonlocal cellular automata

Dynamical systems with nonlocal connections have potential applications to economic and biological systems. This paper studies the dynamics of nonlocal cellular automata. In particular, all two-state, three-input nonlocal cellular automata are classified according to the dynamical behavior starting from random initial configurations and random wirings, although it is observed that sometimes a rule can have different dynamical behaviors with different wirings. The nonlocal cellular automata rule space is studied using a mean-field parametrization which is ideal for the situation of random wiring. Nonlocal cellular automata can be considered as computers carrying out computation at the level of each component. Their computational abilities are studied from the point of view of whether they contain many basic logical gates. In particular, I ask the question of whether a three-input cellular automaton rule contains the three fundamental logical gates: two-input rules AND and OR, and one-input rule NOT. A particularly interesting edge-of-chaos nonlocal cellular automaton, the rule 184, is studied in detail. It is a system of coupled selectors or multiplexers. It is also part of the Fredkin's gate—a proposed fundamental gate for conservative computations. This rule exhibits irregular fluctuations of density, large coherent structures, and long transient times.     

Thes-f model with Coulomb repulsion: Thermodynamics of two atomic cluster. Spin 1/2

A cluster of two atoms described by thes-f model with Coulomb repulsion has been considered. The interaction between localized 4f electrons (S=1/2) is taken in the molecular field approximation. The thermodynamic quantities like magnetization, specific heat and correlation functions n , n , S ^z n , S ^z n , S ^z (n –n ), n n and S ⁺ a ⁺ a as functions of temperature are presented for different band fillingN=0, 0.5, 1, 1.5, 2. The dependence of Curie temperature onN is calculated. The phase diagram forN=1 (T=0K) shows the possibility of existence of two phases: paramagnetic and ferromagnetic.The Curie temperature and the specific heat as functions ofN exhibit similar trends as found in experiments on doped magnetic semiconductors.     

The influence of tensile stress on grain and cell boundary precipitation in supersaturated Al-Zn alloys during creep

The results are presented of the optical microscopic and X-ray diffraction study of the stress-induced nucleation and growth of (Zn) precipitates at grain and cell boundaries (GB's and CB's) during uniaxial creep at 200 °C of supersaturated AlZn20 and AlZn30 alloys. The rate of precipitation is increased mainly owing to the modifying effect of tensile stress on diffusion processes in alloy samples during their anneal. The diffusion of Zn atoms toward GB's and CB's from adjacent regions of grains is accompanied during creep by diffusive flux of Zn along boundaries parallel or nearly parallel to the tensile creep axis toward boundaries with near to normal orientation to that axis. Enhanced precipitation of results then preferentially at the latter and is supressed at the former boundaries where even the dissolution of preexisting has been found during a later application of tensile stress. The stress-induced precipitation of at GB's gradually ceases with prolonged creep exposures due to the lengthening of duffusion paths of Zn atoms from grain interior to GB's.Dissolution of lamellae by their regress toward GB's and CB's is assisted with the stress-induced diffusion of Zn along epitaxial / lamellar interfaces. Copious precipitation of at the parts of GB's and/or CB's with near to normal orientation to the creep axis is then observed on account of Zn from dissolved lamellae. Creep strain also leads to the fragmentation of lamellae and thus also to breaking down of the paths for diffusion of Zn along / interfaces. Spheroidization of fragmented parts of lamellae is then observed. Spheroids of remain embedded within the former lamellar regions.Large creep strains and high strain rates observed on fine-grained alloy samples may be associated with an enhanced viscous GB sliding due to the stress-dependent flow of Zn along GB's and/or CB's.     

Gravity of Global U(1) Cosmic String

We show that a static one-dimensional U(1) global string is confined by its own gravitational field to a finite radius. The energy-momentum tensor of a global string decreases exponentially with the distance from its core. We call it self-localization. We show that the order parameter is a decreasing function of the symmetry breaking energy scale. We have found the maximum value of the energy scale _max, where the order parameter vanishes. Beyond the maximum value > _max the gravitational field of a global string gets so strong, that it restores the initial unbroken symmetry. In the close vicinity of the maximum value _max of the symmetry breaking scale we get a closed-form solution for the metric. It reduces to the Galileo metric on the axis and transforms into the Kasner-type solution near the boundary of a string.     

Conserved moments in nonequilibrium field dynamics

We demonstrate with the example of Cahn-Hilliard dynamics that the macroscopic kinetics of first-order phase transitions exhibits an infinite number of constants of motion. Moreover, this result holds in any space dimension for a broad class of nonequilibrium processes whose macroscopic behavior is governed by equations of the form /t = W(), where is an order parameter,W is an arbitrary function of , and is a linear Hermitian operator. We speculate on the implications of this result.     

Structural properties of aZ(N 2)-spin model and its equivalentZ(N)-vertex model

We show that aZ(N ²)-spin model proposed by A. B. Zamolodchikov and M. I. Monastyrskii can be conveniently described by two interactingN-state Potts models. We study its properties, especially by using a dual invariant quantity of the model. A partial duality performed on one set of Potts spins yields a staggeredZ(N)-symmetric vertex model, which turns out to be a generalization of theN-state nonintersecting string model of C. L. Schultz and J. H. H. Perk. We describe its properties and elaborate on its (pseudo) weak-graph symmetry As by-products we find alternative representations of the N²-state andN-state Potts models by staggered Schultz-Perk vertex models, as compared to the usual representation by staggered six-vertex models.     

A matrix method for estimating the Liapunov exponent of one-dimensional systems

Let : [0, 1][0, 1] be a piecewise monotonie expanding map. Then admits an absolutely continuous invariant measure. A result of Kosyakin and Sandler shows that can be approximated by a sequence of absolutely continuous measures _n invariant under piecewise linear Markov maps _itn. Each _itn is constructed on the inverse images of the turning points of . The easily computable measures _n are used to estimate the Liapunov exponent of . The idea of using Markov maps for estimating the Liapunov exponent is applied to both expanding and nonexpanding maps.     

Microscopic-based fluid flow invasion simulations

A microscopic method for the generation of invasion percolation structures using armies of interacting random walkers is presented. Two distinct species are used to simulate the invading and defending fluids of a fluid invasion process. Trapping of the defending species is accomplished purely by local rules, without the need to repetitively check the connection between the to be displaced defender phase and the sink.     

Matrix Representations for Vector Differential Operators in General Orthogonal Coordinates

The restrictions in arbitrary orthogonal coordinates to a unified matrix presentation of vector operations using generalized differential matrix operators [Y. Chen et al.: IEEE Trans. on Educ., Vol. 41, (1998), p. 61] are pointed out. The corrected matrix representation for the operations (A) and B(A) valid in arbitrary orthogonal curvilinear coordinates are obtained and shown to be consistent with the calculation using the dyadic technique. The presentation is accessible to undergraduate students.     

Long range scattering for nonlinear Schrödinger equations in one space dimension

We consider the scattering problem for the nonlinear Schrödinger equation in 1+1 dimensions: where = /x,R{0},R,p>3. We show that modified wave operators for (*) exist on a dense set of a neighborhood of zero in the Lebesgue spaceL ²(R) or in the Sobolev spaceH ¹(R)., The modified wave operators are introduced in order to control the long range nonlinearity |u|² u.Laboratoire associé au Centre National de la Recherche Scientifique     

Quasicrystal Ising chain and automata theory

An automatic sequence is generated by a finite machine (automaton). These sequences can be periodic or not: in the latter case however, they are not random, but rather quasicrystalline. We consider an Ising chain with variable interaction in a uniform external field, at zero temperature, and prove that, if this interaction is automatic, then the induced magnetic field is also automatic.     

A finite size analysis of the structure factor in the antiferromagnetic Heisenberg (AFH) model

From a finite size analysis we extract the structure factorS(p, N=) of the one dimensional AFH-model in the groundstate: The gross structure is well described byL (p) = –ln(1– ^p ). The fine structure which only contributes a few percent reveals a pronounced non-linear behavior inL(p) with a maximum atp=0.20 and a minimum atp=0.82.     

The Countable Number of Models in the Cosmology with Nonminimal Coupling and Torsion

Cosmological models of flat space with a nonminimally coupled scalar field and ultrarelativistic gas are studied within the Einstein–Kartan theory. Exact general solutions are derived for two-component models and those containing only scalar field for an arbitrary coupling constant . It is shown that both singular and countable number of nonsingular models is possible depending on the type of scalar field and the sign of . The special values of and restrictions on are found for the above solutions. The role of relativistic gas in the evolution of models is revealed.     

Reliable Cellular Automata with Self-Organization

In a probabilistic cellular automaton in which all local transitions have positive probability, the problem of keeping a bit of information indefinitely is nontrivial, even in an infinite automaton. Still, there is a solution in 2 dimensions, and this solution can be used to construct a simple 3-dimensional discrete-time universal fault-tolerant cellular automaton. This technique does not help much to solve the following problems: remembering a bit of information in 1 dimension; computing in dimensions lower than 3; computing in any dimension with non-synchronized transitions. Our more complex technique organizes the cells in blocks that perform a reliable simulation of a second (generalized) cellular automaton. The cells of the latter automaton are also organized in blocks, simulating even more reliably a third automaton, etc. Since all this (a possibly infinite hierarchy) is organized in software, it must be under repair all the time from damage caused by errors. A large part of the problem is essentially self-stabilization recovering from a mess of arbitrary size and content. The present paper constructs an asynchronous one-dimensional fault-tolerant cellular automaton, with the further feature of self-organization. The latter means that unless a large amount of input information must be given, the initial configuration can be chosen homogeneous.     

Stochastic coupling and thermodynamic inequalities

Let ₁ and ₂ be thermodynamic Gibbs measures on ^m and ⁿ , respectively. Diffusions are constructed having ₁, and ₂ as invariant measures. These diffusions are then coupled; inequalities between expectations of certain random variables on the two spaces result.Partially supported by NSF-MCS 74-07313-A03     

Annealed and quenched inhomogeneous cellular automata (INCA)

A probabilistic one-dimensional cellular automaton model by Domany and Kinzel is mapped into an inhomogeneous cellular automaton with the Boolean functions XOR and AND as transition rules. Wolfram's classification is recovered by varying the frequency of these two simple rules and by quenching or annealing the inhomogeneity. In particular, class 4 is related to critical behavior in directed percolation. Also, the critical slowing down of second-order phase transitions is related to a stochastic version of the classical halting problem of computation theory.     

Renewal Sequences and Intermittency

In this paper we examine the generating function (z) of a renewal sequence arising from the distribution of return times in the turbulent region for a class of piecewise affine interval maps introduced by Gaspard and Wang and studied by several authors. We prove that it admits a meromorphic continuation to the entire complex z-plane with a branch cut along the ray (1, +). Moreover, we compute the asymptotic behavior of the coefficients of its Taylor expansion at z=0. From this, we obtain the exact polynomial asympotics for the rate of mixing when the invariant measure is finite and of the scaling rate when it is infinite.     

New two-color dimer models with critical ground states

We define two new models on the square lattice in which each allowed configuration is a superposition of a covering by white dimers and one by black dimers. Each model maps to a solid-on-solid (SOS) model in which the height field is two dimensional. Measuring the stiffness of the SOS fluctuations in the rough phase provides critical exponents of the dimer models. Using this height representation, we have performed Monte Carlo simulations. They confirm that each dimer model has critical correlations and belongs to a new universality class. In the dimer-loop model (which maps to a loop model) one height component is smooth, but has unusual correlated fluctuations; the other height component is rough. In the noncrossing-dimer model the heights are rough, having two different elastic constants; an unusual form of its elastic theory implies anisotropic critical correlations.     

A new procedure for thin-film deposition by solution spraying

The major reasons for the low photovoltaic efficiency of Cu₂S/CdS cells, in which the CdS film is deposited by spraying, are due to small film thicknesses which do not exceed 4 m and the small average grain size which ranges from 0.1 to 0.5 m.A new experimental solution spraying procedure is described that prevents both restrictions by controlling the substrate temperature. Average grain sizes of more than 1 m are obtained.Work supported by Ministere Pubblica Istruzione and Centro Regionale Ricerche Nucleari e di Struttura della Materia     

Pairing correlations: II. Exact model ground-state results for generalised ladders

In this series of papers, the so-called ground-state version of the [exp(S) or] coupled-cluster formalism (CCF) of quantum many-body theory is applied to the general problem of pairing correlations within a many-body system of identical fermions. In this second work in the series we restrict ourselves to exact calculations and concentrate on analytic solutions to the generalised ladder approximations formulated in the first paper. We focus attention on the particular model case of a general (non-local) separable potential, and work within the so-called complete ladder (CLAD) approximation which was shown in the earlier paper to be the CCF formulation of the well-known Galitskii approximation. We show how the CLAD approximation reduces in this case to a highly non-trivial pair of coupled nonlinear integral equations for the four-point correlation function,S ₂, which provides a measure of the two-particle/two-hole component in the true ground-state wave-function. In the further derivation of exact analytic solutions for bothS ₂ and the corresponding ground-state energy, we also see how various types of composite pairs within the many-body medium manifest themselves as virtual (de-)excitations. We thus show how our CCF provides an efficient and unified framework in which to describe all aspects of pairing, such as: (i) a possible free bound pair and its gradual approach to dissolution as the density is increased; (ii) the possible appearance of a second bound pair of predominantly hole-like quasi-particles above some lower critical density (which depends on the total momentum of the pair); (iii) the unstable but bound resonant pairs that can exist for densities above a comparable upper critical density at which the two previous types of real bound pairs have dissolved; and (iv) Cooper pairs. Even though each of these composite pairs leads to a new condensed-pair phase of lower energy, we further show that our so-called ground-state CCF leads only to the fluid-like state of uncondensed particles. In a third paper in this series we use the solutions obtained here as input to the analogous excited-state version of the CCF, and show how these various composite pairs materialise as negative energy (de-)excitations.