Simulation of glioblastoma multiforme (GBM) tumor cells using ising model on the Creutz Cellular Automaton

2017 ◽  
Vol 486 ◽  
pp. 901-907 ◽  
Author(s):  
Artuç Züleyha ◽  
Merdan Ziya ◽  
Yeşiltaş Selçuk ◽  
Öztürk M. Kemal ◽  
Tez Mesut
Keyword(s):  
Glioblastoma Multiforme ◽  
Ising Model ◽  
Cellular Automaton ◽  
Tumor Cells ◽  
Creutz Cellular Automaton

THE SIMULATION OF 2D SPIN-1 ISING MODEL WITH POSITIVE BIQUADRATIC INTERACTION ON A CELLULAR AUTOMATON

2003 ◽  
Vol 14 (10) ◽  
pp. 1305-1320 ◽  
Author(s):  
BÜLENT KUTLU
Keyword(s):  
Phase Transition ◽  
Ising Model ◽  
Cellular Automaton ◽  
Intermediate Phase ◽  
Finite Size ◽  
Square Lattice ◽  
Two Dimensional ◽  
Finite Size Scaling ◽  
Creutz Cellular Automaton ◽  
Antiferromagnetic Spin

The two-dimensional antiferromagnetic spin-1 Ising model with positive biquadratic interaction is simulated on a cellular automaton which based on the Creutz cellular automaton for square lattice. Phase diagrams characterizing phase transition of the model are presented for a comparison with those obtained from other calculations. We confirm the existence of the intermediate phase observed in previous works for some values of J/K and D/K. The values of the static critical exponents (β, γ and ν) are estimated within the framework of the finite-size scaling theory for D/K<2J/K. Although the results are compatible with the universal Ising critical behavior in the region of D/K<2J/K-4, the model does not exhibit any universal behavior in the interval 2J/K-4<D/K<2J/K.

A FINITE-SIZE SCALING STUDY OF THE FOUR-DIMENSIONAL ISING MODEL ON THE CREUTZ CELLULAR AUTOMATON

1999 ◽  
Vol 10 (05) ◽  
pp. 875-881 ◽  
Author(s):  
N. AKTEKIN ◽  
A. GÜNEN ◽  
Z. SAĞLAM
Keyword(s):  
Magnetic Susceptibility ◽  
Ising Model ◽  
Cellular Automaton ◽  
Specific Heat ◽  
Finite Size ◽  
Scaling Relations ◽  
Finite Size Scaling ◽  
Critical Temperatures ◽  
Size Scaling ◽  
Creutz Cellular Automaton

The four-dimensional Ising model is simulated on the Creutz cellular automaton with increased precision. The data are analyzed according to the finite-size scaling relations available. The precision of the critical values related to magnetic susceptibility is improved by one digit, but in order to reach to the same precision for those related to the specific heat more simulation runs at the critical temperatures of the finite-size lattices are required.

Simulation of the Eight-Dimensional Ising Model on the Creutz Cellular Automaton

1997 ◽  
Vol 08 (02) ◽  
pp. 287-292 ◽  
Author(s):  
N. Aktekin
Keyword(s):  
Magnetic Susceptibility ◽  
Renormalization Group ◽  
Critical Temperature ◽  
Ising Model ◽  
Cellular Automaton ◽  
Critical Exponent ◽  
Power Law ◽  
Order Parameter ◽  
Creutz Cellular Automaton

The eight-dimensional Ising model is simulated on the Creutz cellular automaton. By fitting the data for the order parameter to a power law with correction and by using the renormalization group prediction for its leading critical exponent as the criterion, the value of the critical temperature is found as Tc=14.898±0.010 at which the computed value of the leading critical exponent for the magnetic susceptibility is in agreement with the renormalization group prediction.

THE EFFECT OF THE DIPOLE–QUADRUPOLE INTERACTION ON THE PHASE SPACE OF THE SPIN-1 ISING MODEL

2011 ◽  
Vol 25 (09) ◽  
pp. 1211-1224
Author(s):  
A. ÖZKAN ◽  
B. KUTLU
Keyword(s):  
Ising Model ◽  
Cellular Automaton ◽  
Quadrupole Interaction ◽  
Tricritical Point ◽  
Face Centered Cubic ◽  
Fcc Lattice ◽  
Simulation Results ◽  
Face Centered ◽  
Creutz Cellular Automaton ◽  
Special Points

The spin-1 Ising model with the dipole–quadrupole interaction (ℓ = L/J) has been simulated using a cellular automaton (CA) algorithm improved from the Creutz cellular automaton (CCA) for a face-centered cubic (fcc) lattice. The simulations have been made for different ℓ values at the reentrant phase transition and the special points such as the tricritical point (k = K/J = 0, d = D/J = 5.7) and the critical end point (k = -0.9, d = 0.7). The simulation results show that the model has the dense ferromagnetic (df, df(+), df(-)) and the ferromagnetic (F, F(+), F(-)) phases with the dipole–quadrupole interaction. The type and the order of the phase transitions change for the nonzero values of ℓ on the special points. Furthermore, the effect of ℓ is similar with the effect of the external magnetic field (h).

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