Determination of fixed points and shift cycles for nearest neighbor cellular automata

One-dimensional nearest neighbor cellular automata defined over Z₂ are characterized in terms of a set of eight nonadditive basis operators which act on the automaton state space. Every evolution rule for such automata can be expressed as an operator which is a direct sum of the basis operators. This approach allows decomposition of automata rules into additive and nonadditive parts. As a result, it is simple to determine fixed points (those states for which the rule reduces to the identity), and shift cycles (sets of states on which the rule reduces to a shift). Sets of states on which any given nearest neighbor automaton reduces to an identity or a shift are characterized. This allows us to obtain some results on the entropic properties of nonadditive automata, although these are not nearly so complete as results obtained for additive automata.     

Supervised nuclear track detection of CR-39 detectors by cellular automata

In this paper, cellular automata are used to detect the nuclear tracks in the track images captured from the surface of CR-39 detectors. Parameters of the automaton as the states, neighborhood, rules and quality parameters are defined optimally for the track image data set under analysis. The presented method is a supervised computational algorithm which comprises a rule definition phase as the learning procedure. Parameter optimization is also performed to adapt the algorithm to the data set used.     

Response of triafol-TN plastic track detectors to238U-ions

Triafol-TN plastic detector foils have been irradiated with²³⁸U ions of energy 16.34 MeV/u and the tracks produced have been observed using the chemical etching technique. The bulk etch rate and track etch rate are determined under successive chemical etching. In our case, the validity of Arrhenius’s law is confirmed by the fact that the same value ofE _a obtained for these different concentrations, within experimental errors. The results show a linear correlation between the measured track etch rate along the track and the corresponding total energy loss rate and a threshold value of ～ 5.0 MeV/(mg/cm²) for track registration was obtained. The maximum etched track length of²³⁸U-ion in triafol-TN has been compared with the theoretically computed range.     

Index Theory of One Dimensional Quantum Walks and Cellular Automata

If a one-dimensional quantum lattice system is subject to one step of a reversible discrete-time dynamics, it is intuitive that as much “quantum information” as moves into any given block of cells from the left, has to exit that block to the right. For two types of such systems — namely quantum walks and cellular automata — we make this intuition precise by defining an index, a quantity that measures the “net flow of quantum information” through the system. The index supplies a complete characterization of two properties of the discrete dynamics. First, two systems S ₁, S ₂ can be “pieced together”, in the sense that there is a system S which acts like S ₁ in one region and like S ₂ in some other region, if and only if S ₁ and S ₂ have the same index. Second, the index labels connected components of such systems: equality of the index is necessary and sufficient for the existence of a continuous deformation of S ₁ into S ₂. In the case of quantum walks, the index is integer-valued, whereas for cellular automata, it takes values in the group of positive rationals. In both cases, the map \({S \mapsto {\rm ind} S}\) is a group homomorphism if composition of the discrete dynamics is taken as the group law of the quantum systems. Systems with trivial index are precisely those which can be realized by partitioned unitaries, and the prototypes of systems with non-trivial index are shifts.     

Complex dynamics of cellular automata rule 119

In this paper, the dynamical behaviors of cellular automata rule 119 are studied from the viewpoint of symbolic dynamics in the bi-infinite symbolic sequence space Σ₂. It is shown that there exists one Bernoulli-measure global attractor of rule 119, which is also the nonwandering set of the rule. Moreover, it is demonstrated that rule 119 is topologically mixing on the global attractor and possesses the positive topological entropy. Therefore, rule 119 is chaotic in the sense of both Li-Yorke and Devaney on the global attractor. It is interesting that rule 119, a member of Wolfram’s class II which was said to be simple as periodic before, actually possesses a chaotic global attractor in Σ₂. Finally, it is noted that the method presented in this work is also applicable to studying the dynamics of other rules, especially the 112 Bernoulli-shift rules therein.     

Study of surface morphology of ferrofluid deposited etched ion tracks in dielectric layers

An AFM study is reported on swift heavy irradiated Si/SiO₂ substrates which have been etched by aqueous hydrofluoric acid solution leading to ion tracks in which ferrofluids have been deposited leading to tunable electronic materials with pores in oxide on silicon (TEMPOS) structure. Two ferrofluids with different carrier fluids (aqueous and non-aqueous) have been deposited in the tracks. Atomic force microscopy has been used to study the empty as well as filled tracks. Since the ferrofluids contain iron oxide particles, there is a possibility of agglomeration of these particles inside and outside the tracks. Surface area and pore volume of the tracks have been measured by Brunauer-Emmett-Teller (BET) method. The track properties (empty and filled) as observed by AFM have been correlated with BET measurements.     

Dynamic transitions in Domany-Kinzel cellular automata on small-world network

We study Domany-Kinzel cellular automata on small-world network. Every link on a one dimensional chain is rewired and coupled with any node with probability p. We observe that, the introduction of long-range interactions does not remove the critical character of the model and the system still exhibits a well-defined phase transition to absorbing state. In case of directed percolation (DP), we observe a very anomalous behavior as a function of size. The system shows long lived metastable states and a jump in order parameter. This jump vanishes in thermodynamic limit and we recover second-order transition. The critical exponents are not equal to the mean-field values even for large p. However, for compact directed percolation(CDP), the critical exponents reach their mean-field values even for small p.     

A new method to measure track density and to differentiate nuclear tracks in CR-39 detectors

An alternative method to count and differentiate nuclear tracks in SSNTD is described. The method is based on the analysis of Fraunhofer diffraction pattern of coherent light produced by tracks of an etched SSNT detector. The diffraction pattern was also simulated by applying computational Fourier Optics. The comparison between results obtained by simulation and by the theoretical model gave satisfactory concordance. The proposed method is capable of differentiating tracks in CR-39 by their diameter and energies. The diameter resolution ranged between 8% and 25%, while the counting error was less than 15%. The discriminating ability to distinguish genuine etched tracks from defects and background anomalies is demonstrated. The incidence angle did not influence significantly the total count and the track parameter measuring capability. Errors due to track overlapping are only significant for track densities higher than 3×10⁵ cm⁻².     

SHI induced nano track polymer filters and characterization

Swift heavy ion irradiation produces damage in polymers in the form of latent tracks. Latent tracks can be enlarged by etching it in a suitable etchant and thus nuclear track etch membrane can be formed for gas permeation / purification in particular for hydrogen where the molecular size is very small. By applying suitable and controlled etching conditions well defined tracks can be formed for specific applications of the membranes. After etching gas permeation method is used for characterizing the tracks. In the present work polycarbonate (PC) of various thickness were irradiated with energetic ion beam at Inter University Accelerator Centre (IUAC), New Delhi. Nuclear tracks were modified by etching the PC in 6N NaOH at 60 (±1) °C from both sides for different times to produce track etch membranes. At critical etch time the etched pits from both the sides meet a rapid increase in gas permeation was observed. Permeability of hydrogen and carbon dioxide has been measured in samples etched for different times. The latent tracks produced by SHI irradiation in the track etch membranes show enhancement of free volume of the polymer. Nano filters are separation devices for the mixture of gases, different ions in the solution and isotopes and isobars separations. The polymer thin films with controlled porosity finding it self as best choice. However, the permeability and selectivity of these polymer based membrane filters are very important at the nano scale separation. The Swift Heavy Ion (SHI) induced nuclear track etched polymeric films with controlled etching have been attempted and characterized as nano scale filters.      

From PCA's to equilibrium systems and back

Stationary measures for probabilistic cellular automata (PCA's) ind dimensions give rise to space-time histories whose statistics may naturally be described by Gibbs states ind+1 dimensions for an interaction energy ? obtained from the PCA. In this note we study the converse question: Do all Gibbs states for this ? correspond to statistical space-time histories for the PCA? Our main result states that the answer is yes, at least for translation invariant or periodic Gibbs states. Thus ergodicity questions for PCA's can, at least partially, be formulated as questions of uniqueness of Gibbs states.     

The electrochemistry of InP in Br2/HBr solutions and its relevance to etching behaviour

Etch rate-potential curves of p-InP in HBrandBr₂/HBr solutions in the dark and under illumination were correlated with current-potential curves. It was found that InP is etched via a “chemical” mechanism both by HBrandBr₂. In aqueous HBr solutions InP is only etched at a significant rate at concentrations higher than 5 mol/ℓ. The Br₂ etchants contained 4.5M HBr; in this case HBr only serves to complex Br₂toBr^-₃. The etch rate in Br₂/HBr solutions is mass-transport controlled at InP(001) and kinetically controlled at InP with the (111) In orientation. The macroscopically obtained results are consistent with the profiles etched at resist edges in InP. The electrochemistry of Br₂ at p-InP under illumination reveals some interesting aspects with regard to the agreement between the etch rate and the Br₂ reduction.     

Reversibility of 1D Cellular Automata with Periodic Boundary over Finite Fields $\pmb{ {\mathbb{Z}}}_{p}$

The reversibility problem for linear cellular automata with null boundary defined by a rule matrix in the form of a pentadiagonal matrix was studied recently over the binary field ℤ₂ (del Rey and Rodriguez Sánchez in Appl. Math. Comput., 2011, doi:). In this paper, we study one-dimensional linear cellular automata with periodic boundary conditions over any finite field ℤ _p . For any given p≥2, we show that the reversibility problem can be reduced to solving a recurrence relation depending on the number of cells and the coefficients of the local rules defining the one-dimensional linear cellular automata. More specifically, for any given values (from any fixed field ℤ _p ) of the coefficients of the local rules, we outline a computer algorithm determining the recurrence relation which can be solved by testing reversibility of the cellular automaton for some finite number of cells. As an example, we give the full criteria for the reversibility of the one-dimensional linear cellular automata over the fields ℤ₂ and ℤ₃.     

Polarons in alkaline-earth-like atoms with multiple background Fermi surfaces

We study the impurity problem in a Fermi gas of ¹⁷³Yb atoms near an orbital Feshbach resonance (OFR), where a single moving particle in the ³P₀ state interacts with two background Fermi seas of particles in different nuclear states of the ground ¹S₀ manifold. By employing wave function ansatz to molecule and polaron states, we investigate various properties of the molecule, the attractive polaron, and the repulsive polaron states. In comparison to the case where only one Fermi sea is populated, we find that the presence of an additional Fermi sea acts as an energy shift between the two channels of the OFR. In addition, quantum fluctuations near the Fermi level can also induce sizable effects to various properties of the attractive and repulsive polarons.     

Investigation of latent and short etched heavy ion tracks in solids

In the past five years were carried out SANS (Small-Angle Neutron Scattering measurements in the JINR to investigate latent and short etched tracks in SSNTD. The results demonstrate the suitability of the method to study not etched and short etched tracks to analyse the etching process, e.g. for nuclear track filter production. The results are in good agreement with other methods as conductivity measurements.     

Propagation of fronts in cellular automata

The problem of propagation of fronts (traveling fronts) is investigated for two classes of two-dimensional cellular automata: simple totalistic automata with states 0,1, and Greenberg-Hastings automata that minic infection processes. These automata are investigated with analytic and with simulation methods. In the deterministic case the exact shapes of (anisotropic) fronts are determined as well as the propagation speed in several directions. In the stochastic case the fronts are investigated by simulation.     

Fast-neutron spectroscopy studies using induced-proton tracks in PADC track detectors

In this work, a simple and adequate method for fast-neutron spectroscopy is proposed. This method was performed by free-in-air fast-neutron irradiation of CR-39 Nuclear Track Detectors (NTD) using an Am-Be source. Detectors were then chemically etched to remove few layers up to a thickness of 6.25 μm. By using an automatic image analyzer system for studying the registration of the induced-proton tracks in the NTD, the obtained data were analyzed via two tracks shapes. In the first one, the elliptical tracks were eliminated from the calculation and only the circular ones were considered in developing the response function. In the second method all registered tracks were considered and the corresponding response function was obtained. The rate of energy loss of the protons as a function of V[(dE/dX) - V] was calculated using the Monte Carlo simulation. The induced-proton energy was extracted from the corresponding dE/dX in NTD using a computer program based on the Bethe-Bloch function. The energy of the incident particles was up to few hundred MeV/nucleon. The energy of the interacting neutrons was then estimated by means of the extracted induced-proton energies and the scattering angle. It was found that the present resulting energy distribution of the fast-neutron spectrum from the Am-Be source was similar to that given in the literature where an average neutron energy of 4.6MeV was obtained.     

Superfluid states in β-stable nuclear matter

Two superfluid states of nuclear matter, which are supposed to play an important role in neutron stars, are discussed: the first one due to the proton-proton ¹ S ₀ pairing in β-equilibrium nuclear matter; the second one due to the anisotropic neutron-neutron ³ PF ₂ pairing in neutron matter. Since the two phases appear at high density of nuclear matter, the three-body forces were added to the pairing interaction and the strong correlation effects in the single-paricle spectrum. The energy gaps, obtained solving the extended BCS equations, significantly deviate from the values without medium effects so as to limit the role of these two superfluid states in the interpretation of phenomena occurring in the neutron-star core.     

Evidence for planar events and a forward double jet structure in deep inelastic Muon scattering

The final states of charged hadrons produced in 280 GeV μp scattering are analysed with respect to their planarity and jet structure. Distributions of p_⊥² in and p_{⊥ out}² are presented. A two jet structure in the forward hemisphere is observed for events with high p_⊥ tracks are predicted by QCD models.     

High-resolution nuclear track mapping in detailed cellular histology using CR-39 with the contact microscopy technique

In radiation cancer therapies using energetic charged particles such as proton/heavy-ion therapy and boron neutron capture therapy (BNCT), studies on radiation-induced biological response at cellular level are important because the radiation damage from energetic charged particles is highly localized along their paths and the radiation sensitivity is quite different in each cellular organelle. In such studies the information on the position of charged particle impact in biological cells is necessary. A novel method for high-resolution nuclear track mapping in detailed cellular histology has been developed. In this technique, biological specimens mounted on CR-39 plates are exposed to energetic charged particles. The irradiated samples are exposed to UV, and then etched for a short time. Both etch pits of nuclear tracks and relief for transmission UV image of the specimen can be observed on the CR-39 surface with an atomic force microscope (AFM) at about 100 nm resolution.