Complex dynamics of elementary cellular automata emerging from chaotic rules

We show techniques of analyzing complex dynamics of cellular automata (CA) with chaotic behaviour. CA are well known computational substrates for studying emergent collective behaviour, complexity, randomness and interaction between order and chaotic systems. A number of attempts have been made to classify CA functions on their space-time dynamics and to predict behaviour of any given function. Examples include mechanical computation, \lambda{} and Z-parameters, mean field theory, differential equations and number conserving features. We aim to classify CA based on their behaviour when they act in a historical mode, i.e. as CA with memory. We demonstrate that cell-state transition rules enriched with memory quickly transform a chaotic system converging to a complex global behaviour from almost any initial condition. Thus just in few steps we can select chaotic rules without exhaustive computational experiments or recurring to additional parameters. We provide analysis of well-known chaotic functions in one-dimensional CA, and decompose dynamics of the automata using majority memory exploring glider dynamics and reactions

Cellular automaton supercolliders

Gliders in one-dimensional cellular automata are compact groups of non-quiescent and non-ether patterns (ether represents a periodic background) translating along automaton lattice. They are cellular-automaton analogous of localizations or quasi-local collective excitations travelling in a spatially extended non-linear medium. They can be considered as binary strings or symbols travelling along a one-dimensional ring, interacting with each other and changing their states, or symbolic values, as a result of interactions. We analyse what types of interaction occur between gliders travelling on a cellular automaton `cyclotron' and build a catalog of the most common reactions. We demonstrate that collisions between gliders emulate the basic types of interaction that occur between localizations in non-linear media: fusion, elastic collision, and soliton-like collision. Computational outcomes of a swarm of gliders circling on a one-dimensional torus are analysed via implementation of cyclic tag systems

Note: "Lock-in accelerometry" to follow sink dynamics in shaken granular matter

Understanding the penetration dynamics of intruders in granular beds is relevant not only for fundamental Physics, but also for geophysical processes and construction on sediments or granular soils in areas potentially affected by earthquakes. While the penetration of intruders in two dimensional (2D) laboratory granular beds can be followed using video recording, it is useless in three dimensional (3D) beds of non-transparent materials such as common sand. Here we propose a method to quantify the sink dynamics of an intruder into laterally shaken granular beds based on the temporal correlations between the signals from a reference accelerometer fixed to the shaken granular bed, and a probe accelerometer deployed inside the intruder. Due to its analogy with the working principle of a lock in amplifier, we call this technique Lock in accelerometry (LIA). During Earthquakes, some soils can lose their ability to sustain shear and deform, causing subsidence and sometimes substantial building damage due to deformation or tumblin

Spin-orbit induced mixed-spin ground state in RRNiO3_3 perovskites probed by XAS: new insight into the metal to insulator transition

We report on a Ni L$_{2,3}$ edges x-ray absorption spectroscopy (XAS) study in $R$NiO$_3$ perovskites. These compounds exhibit a metal to insulator ($MI$) transition as temperature decreases. The L$_{3}$ edge presents a clear splitting in the insulating state, associated to a less hybridized ground state. Using charge transfer multiplet calculations, we establish the importance of the crystal field and 3d spin-orbit coupling to create a mixed-spin ground state. We explain the $MI$ transition in $R$NiO$_3$ perovskites in terms of modifications in the Ni$^{3+}$ crystal field splitting that induces a spin transition from an essentially low-spin (LS) to a mixed-spin state.Comment: 4 pages, 4 figures, accepted as PRB - Rapid Comm. Dez. 200

First order transition and phase separation in pyrochlores with colossal-magnetoresistance

Tl$_{2}$Mn$_{2}$O$_{7}$ pyrochlores present colossal magnetoresistance (CMR) around the long range ferromagnetic ordering temperature (T$_{C}$). The character of this magnetic phase transition has been determined to be first order, by purely magnetic methods, in contrast to the second order character previously reported by Zhao et al. (Phys. Rev. Lett. 83, 219 (1999)). The highest CMR effect, as in Tl$_{1.8}$Cd$_{0.2}$Mn$_{2}$O$_{7}$, corresponds to a stronger first order character. This character implies a second type of magnetic interaction, besides the direct superexchange between the Mn$^{4+}$ ions, as well as a phase coexistence. A model is proposed, with a complete Hamiltonian (including superexchange and an indirect interaction), which reproduce the observed phenomenology.Comment: 6 pages. Figures include

Short-range charge-order in RRNiO3_{3} perovskites (RR=Pr,Nd,Eu) probed by X-ray absorption spectroscopy

The short-range organization around Ni atoms in orthorhombic $R$NiO$_{3}$ ($R$=Pr,Nd,Eu) perovskites has been studied over a wide temperature range by Ni K-edge x-ray absorption spectroscopy. Our results demonstrate that two different Ni sites, with different average Ni-O bond lengths, coexist in those orthorhombic compounds and that important modifications in the Ni nearest neighbors environment take place across the metal-insulator transition. We report evidences for the existence of short-range charge-order in the insulating state, as found in the monoclinic compounds. Moreover, our results suggest that the two different Ni sites coexists even in the metallic state. The coexistence of two different Ni sites, independently on the $R$ ion, provides a common ground to describe these compounds and shed new light in the understanding of the phonon-assisted conduction mechanism and unusual antiferromagnetism present in all $R$NiO$_{3}$ compounds.Comment: 4 pages, 3 figures, accepted PRB - Brief Report Dec.200

Aquifer vulnerability mapping and associated spatial uncertainty

Quantitative estimation of water resources is indispensable when it comes to getting the sustainability of aquifers through planning. This becomes an essential aspect in areas whose primary economic activity is agriculture, in which ensure the availability of water means ensuring the sustainability of the societal and economic systems. This is the example of the Cuellar Moor karstic aquifer, located in the international Duero watershed, in which more than 80% of its surface is aimed to agricultural use. The main goal of this research is the introduction of a new vulnerability index, which gathers together the hydrogeological covariates and the spatial uncertainty associated with the estimation of groundwater level and nitrate concentration. An optimized monitoring network to piezometric level and nitrate concentration control is required, as well as, to determine the vulnerability associated with pumping wells.info:eu-repo/semantics/publishedVersio

A Classification of Integrable Quasiclassical Deformations of Algebraic Curves

A previously introduced scheme for describing integrable deformations of of algebraic curves is completed. Lenard relations are used to characterize and classify these deformations in terms of hydrodynamic type systems. A general solution of the compatibility conditions for consistent deformations is given and expressions for the solutions of the corresponding Lenard relations are provided.Comment: 21 page

Electrical control of a laterally ordered InAs/InP quantum dash array

We have fabricated an array of closely spaced quantum dashes starting from a planar array of self-assembled semiconductor quantum wires. The array is embedded in a metallic nanogap which we investigate by micro-photoluminescence as a function of a lateral electric field. We demonstrate that the net electric charge and emission energy of individual quantum dashes can be modified externally with performance limited by the size inhomogeneity of the self-assembling process