<i>Computational Physics: Problem Solving with Computers</i>

Landau, Rubin H.; Páez, Manuel J.; Kowallik, Hans; Jansen, Henricus V.

doi:10.1063/1.882306

Cited by 57 publications

(68 citation statements)

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“…Thus, in order to generalize the study of the properties of this model by a nonextensive approach, we modified the Metropolis method for the nonextensive statistics. To proceed the single spin flip MC calculations [36] and to obtain the physical quantities of interest of the system (magnetization, susceptibility, specific heat, and other quantities), we have changed the usual statistical weight to [21] w q = P i,af ter…”

Section: Nonextensive Statistics and Monte Carlo Simulationmentioning

confidence: 99%

Finite-size analysis of a two-dimensional Ising model within a nonextensive approach

Crokidakis¹,

Soares-Pinto²,

Reis³

et al. 2009

Phys. Rev. E

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In this work we present a thorough analysis of the phase transitions that occur in a ferromagnetic 2D Ising model, with only nearest-neighbors interactions, in the framework of the Tsallis nonextensive statistics. We performed Monte Carlo simulations on square lattices with linear sizes L ranging from 32 up to 512. The statistical weight of the Metropolis algorithm was changed according to the nonextensive statistics. Discontinuities in the m(T) curve are observed for q ≤ 0.5. However, we have verified only one peak on the energy histograms at the critical temperatures, indicating the occurrence of continuous phase transitions. For the 0.5 < q ≤ 1.0 regime, we have found continuous phase transitions between the ordered and the disordered phases, and determined the critical exponents via finite-size scaling. We verified that the critical exponents α, β and γ depend on the entropic index q in the range 0.5 < q ≤ 1.0 in the form α(q) = (10 q 2 − 33 q + 23)/20, β(q) = (2 q − 1)/8 and γ(q) = (q 2 − q + 7)/4. On the other hand, the critical exponent ν does not depend on q. This suggests a violation of the scaling relations 2 β + γ = d ν and α + 2 β + γ = 2 and a nonuniversality of the critical exponents along the ferro-paramagnetic frontier.

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Section: Nonextensive Statistics and Monte Carlo Simulationmentioning

confidence: 99%

Finite-size analysis of a two-dimensional Ising model within a nonextensive approach

Crokidakis¹,

Soares-Pinto²,

Reis³

et al. 2009

Phys. Rev. E

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“…Based on this information, one can obtain the positions r in+1/2 , corresponding to the midpoint of the integration interval h (Euler method The energy conservation is not explicitly built in the algorithm. The precision could be thus checked by plotting [1] …”

Section: Program Descriptionmentioning

confidence: 99%

“…The equations (1) are solved using a second order Runge-Kutta algorithm [1]. We calculated first the resultant force F i (t n ) acting on each particle.…”

Section: Program Descriptionmentioning

confidence: 99%

“…Based on a second order Runge-Kutta algorithm [1], we developed a code library for the simulation of relativistic many-body systems [2]. Our attention was mainly focused on both creating a general object oriented solution [1,3,4], easy to customize and extend through the inheritance and polymorphism mechanisms, and developing a set of tools for analyzing the chaotic behavior of many-body systems.…”

Section: Introductionmentioning

confidence: 99%

“…Our attention was mainly focused on both creating a general object oriented solution [1,3,4], easy to customize and extend through the inheritance and polymorphism mechanisms, and developing a set of tools for analyzing the chaotic behavior of many-body systems.…”

Section: Introductionmentioning

confidence: 99%

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Code C# for chaos analysis of relativistic many-body systems

Grossu

Beşliu

Jipa

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This work presents a new Microsoft Visual C# .NET code library, conceived as a general object oriented solution for chaos analysis of three-dimensional, relativistic many-body systems. In this context, we implemented the Lyapunov exponent and the "fragmentation level" (defined using the graph theory and the Shannon entropy). Inspired by existing studies on billiard nuclear models and clusters of galaxies, we tried to apply the virial theorem for a simplified many-body system composed by nucleons. A possible application of the "virial coefficient" to the stability analysis of chaotic systems is also discussed. Program summary

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Modeling the separation of macromolecules: A review of current computer simulation methods

et al. 2009

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Theory and numerical simulations play a major role in the development of improved and novel separation methods. In some cases, computer simulations predict counterintuitive effects that must be taken into account in order to properly optimize a device. In other cases, simulations allow the scientist to focus on a subset of important system parameters. Occasionally, simulations even generate entirely new separation ideas! In this article, we review the main simulation methods that are currently being used to model separation techniques of interest to the readers of Electrophoresis. In the first part of the article, we provide a brief description of the numerical models themselves, starting with molecular methods and then moving towards more efficient coarse-grained approaches. In the second part, we briefly examine nine separation problems and some of the methods used to model them. We conclude with a short discussion of some notoriously hard-to-model separation problems and a description of some of the available simulation software packages.

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Computational Physics: Problem Solving with Computers

Cited by 57 publications

References 0 publications

Finite-size analysis of a two-dimensional Ising model within a nonextensive approach

Finite-size analysis of a two-dimensional Ising model within a nonextensive approach

Code C# for chaos analysis of relativistic many-body systems

Modeling the separation of macromolecules: A review of current computer simulation methods

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