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Nonequilibrium model on Archimedean lattices

100%

Lima F.

Open Physics

2014

tom 12

nr 3

185-191

On (4, 6, 12) and (4, 82) Archimedean lattices, the critical properties of the majority-vote model are considered and studied using the Glauber transition rate proposed by Kwak et al. [Kwak et al., Phys. Rev. E, 75, 061110 (2007)] rather than the traditional majority-vote with noise [Oliveira, J. Stat. Phys. 66, 273 (1992)]. We obtain T c and the critical exponents for this Glauber rate from extensive Monte Carlo studies and finite size scaling. The calculated values of the critical temperatures and Binder cumulant are T c = 0.651(3) and U 4* = 0.612(5), and T c = 0.667(2) and U 4* = 0.613(5), for (4, 6, 12) and (4, 82) lattices respectively, while the exponent (ratios) β/ν, γ/ν and 1/ν are respectively: 0.105(8), 1.48(11) and 1.16(5) for (4, 6, 12); and 0.113(2), 1.60(4) and 0.84(6) for (4, 82) lattices. The usual Ising model and the majority-vote model on previously studied regular lattices or complex networks differ from our new results.

Concentration compactness results for systems in the Heisenberg group

100%

Pucci P. , Temperini L.

Opuscula Mathematica

2020

tom Vol. 40, no. 1

151--163

In this paper we complete the study started in [P. Pucci, L. Temperini, Existence for (p,q) critical systems in the Heisenberg group, Adv. Nonlinear Anal. 9 (2020), 895-922] on some variants of the concentration-compactness principle in bounded PS domains Ω of the Heisenberg group [formula]. The concentration-compactness principle is a basic tool for treating nonlinear problems with lack of compactness. The results proved here can be exploited when dealing with some kind of elliptic systems involving critical nonlinearities and Hardy terms.

Existence and multiplicity results for quasilinear equations in the Heisenberg group

100%

Pucci P.

Opuscula Mathematica

2019

tom Vol. 39, no. 2

247--257

In this paper we complete the study started in [Existence of entire solutions for quasilinear equations in the Heisenberg group, Minimax Theory Appl. 4 (2019)] on entire solutions for a quasilinear equation [formula] in Hn, depending on a real parameter λ, which involves a general elliptic operator A in divergence form and two main nonlinearities. Here, in the so called sublinear case, we prove existence for all λ > 0 and, for special elliptic operators A, existence of infinitely many solutions [formula].

Entire solutions for some critical equations in the Heisenberg group

100%

Pucci P. , Temperini L.

Opuscula Mathematica

2022

tom Vol. 42, no. 2

279--303

We complete the study started in the paper [P. Pucci, L. Temperini, On the concentration-compactness principle for Folland-Stein spaces and for fractional horizontal Sobolev spaces, Math. Eng. 5 (2023), Paper no. 007], giving some applications of its abstract results to get existence of solutions of certain critical equations in the entire Heinseberg group. In particular, different conditions for existence are given for critical horizontal p-Laplacian equations.

The Test of a New Critical Exponent Ϙ by Using Ising Model on the Creutz Cellular Automaton

88%

Merdan Z. , Gokbel-Keklikoglu D.

Acta Physica Polonica A

2018

tom 133

nr 5

1200-1204

Above the upper critical dimension d_{c} the Ising model is simulated on the Creutz cellular automaton. The values of a new critical exponent Ϙ are obtained by using the simulations for the order parameter and the magnetic susceptibility. At d=4,5,6,7,8, the values of the new critical exponent Ϙ are 0.9904(16), 1.2721(2), 1.4806(24), 1.7626(17), 1.9997(50) for the order parameter, respectively, while those 1.0415(13), 1.2987(27), 1.5133(1), 1.7741(1), 2.0133(28) are for the magnetic susceptibility in the same order. The computed values of the new critical exponent Ϙ are in agreement with theoretical values.

Nematic ordering problem as the polymer problem of the excluded volume

75%

Yakunin A.

Open Physics

2003

tom 1

nr 2

355-362

Based on a solution of the polymer excluded volume problem, a technique is proposed to estimate some parameters at the isotropic-nematic liquid crystal phase transition (the product of the volume fraction of hard sticks and the ratio of the stick length, L, to its diameter, D; the maximum value of this ratio at which one cannot regard the stick as hard). The critical exponents are estimated. The transition of a swelling polymer coil to ideal is revealed as the polymerization degree of a macromolecule increases. The entanglement concentration obtained agrees with experimental data for polymers with flexible chains. The number of monomers between neighbor entanglements is assumed to be the ratio L/D. A comparison of the theory with other ones and recent experimental data is made.