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One-Dimensional Cellular Automata with Reflective Boundary Conditions and Radius Three

100%
Akin H., Siap I., Uguz S.
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vol. 125
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issue 2
405-407
EN
A family of one-dimensional finite linear cellular automata with reflective boundary condition over the field Z_p is defined. The generalizations are the radius and the field that states take values. Here, we establish a connection between reversibility of cellular automata and the rule matrix of the cellular automata with radius three. Also, we prove that the reverse CA of this family again falls into this family.
2
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2-Dimensional Reversible Hexagonal Cellular Automata with Periodic Boundary

100%
Uguz S., Siap I., Akin H.
Acta Physica Polonica A
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2013
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vol. 123
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issue 2
480-483
EN
In this paper, we study 2-dimensional finite cellular automata defined by hexagonal local rule with periodic boundary over the field Z_3. We construct the rule matrix corresponding to the hexagonal cellular automata. For some given coefficients and the number of columns of hexagonal information matrix, we prove that the hexagonal cellular automata are reversible.
3
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Description of Extreme Gibbs Measures for the Ising Model with Three Interactions

100%
Akin H., Ganikhodjaev N., Temir S., Uguz S.
Acta Physica Polonica A
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2013
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vol. 123
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issue 2
484-487
EN
In this paper, we consider an Ising model with three competing interactions (nearest neighbor, next-nearest neighbor, and ternary prolonged neighbor) on the Cayley tree of order two, investigated by Ganikhodjaev et al. We study translation-invariant Gibbs measures of the Ising model with these competing interactions. Also, we investigate the set of the extreme Gibbs measures called Markov random fields with memory 2 of the model.
4
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Behavior of the Phase Diagrams of Potts Model οn Cayley Tree for Order Three

100%
Temir S., Ganikhodjaev N., Uguz S., Akin H.
Acta Physica Polonica A
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2013
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vol. 123
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issue 2
476-479
EN
The aim of this paper is to extend the results of Ganikhodjaev et al. to the three state Potts model with competing nearest-neighbor, prolonged next-nearest-neighbor and two-level triple neighbor interactions on a Cayley tree for order 3 and compare with the phase diagrams obtained in Temir et al. and to study modulated phases arising from the frustration effects introduced by nearest-neighbor, prolonged next-nearest-neighbor and two-level triple neighbor interactions.
5
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Characterization of 2D Hybrid Cellular Automata with Periodic Boundary

100%
Acar E., Uguz S., Akin H.
Acta Physica Polonica A
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2017
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vol. 131
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issue 3
432-436
EN
We investigate main theoretical aspects of two-dimensional linear-hybrid cellular automata with periodic boundary condition over the Galois field GF(2). We focus on the characterization of two-dimensional hybrid linear cellular automata by way of a special algorithm. Here we set up a relation between reversibility of cellular automata and characterization of two-dimensional hybrid linear cellular automata with a special boundary conditions, i.e. periodic case. The determination of the characterization problem of special type of cellular automaton is studied by means of the matrix algebra theory. It is believed that this type of cellular automata could find many different applications in special case situations, e.g. image processing area, textile design, video processing, DNA research, etc., in the near future.
6
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2D Cellular Automata with an Image Processing Application

100%
Uguz S., Sahin U., Siap I., Akin H.
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vol. 125
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issue 2
435-438
EN
This paper investigates the theoretical aspects of two-dimensional linear cellular automata with image applications. We consider geometrical and visual aspects of patterns generated by cellular automata evolution. The present work focuses on the theory of two-dimensional linear cellular automata with respect to uniform periodic and adiabatic boundary cellular automata conditions. Multiple copies of any arbitrary image corresponding to cellular automata find so many applications in real life situation e.g. textile design, DNA genetics research, etc.
7
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Behaviors of Phase Diagrams of Ising Model with Competing Ternary and Binary Interactions on a Cayley Tree of Arbitrary Order

100%
Akin H., Ganikhodjaev N., Uguz S., Temir S.
Acta Physica Polonica A
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2012
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vol. 121
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issue 1
104-107
EN
An Ising model with competing interactions has recently been studied extensively because of the appearance of nontrivial magnetic orderings. In this paper, we study the phase diagrams for the Ising model on a Cayley tree with competing nearest-neighbor interactions J and ternary prolonged interactions J_{t_{p}} on a Cayley tree of arbitrary order k and compare with the phase diagrams obtained in Uguz et al. and Vannimenus results for the Ising model on a Cayley tree with competing nearest-neighbor interactions J and ternary prolonged interactions J_{p}. For some values of k, we obtain phase diagrams of the model. We clarify the role of order k of the Cayley tree. We also plot the variation of the wave vector with temperature.
8
Content available remote

The Competing Interactions on a Cayley Tree-Like Lattice: Pentagonal Chandelier

100%
Uguz S., Ganikhodjaev N., Akin H., Temir S.
Acta Physica Polonica A
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2012
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vol. 121
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issue 1
114-118
EN
Different types of lattice spin systems with competing interactions have rich and interesting phase diagrams. In this study we present some new results for such systems involving the Ising spin system (i.e. σ = ± 1) using a generalization of the Cayley tree-like lattice approximation. We study the phase diagrams for the Ising model on a Cayley tree-like lattice, a new lattice type called pentagonal chandelier, with competing nearest-neighbor interactions J_1, prolonged next-nearest-neighbor interactions J_{p} and one-level next-nearest-neighbor senary interactions J_{l_1}^{(6)}. The colored phase diagrams contain some multicritical Lifshitz points that are at nonzero temperature and many modulated new phases. We also investigate the variation of the wave vector with temperature in the modulated phase and the Lyapunov exponent associated with the trajectory of the system.
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