| 1. |
- Ardelius, John, et al.
(författare)
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Clustering of solutions in hard satisfiability problems
- 2007
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Ingår i: Journal of Statistical Mechanics: Theory and Experiment. - 1742-5468. ; :10, s. P10012-
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Tidskriftsartikel (refereegranskat)abstract
- We study numerically the solution space structure of random 3-SAT problems close to the SAT/UNSAT transition. This is done by considering chains of satisfiability problems, where clauses are added sequentially to a problem instance. Using the overlap measure of similarity between different solutions found on the same problem instance, we examine geometrical changes as a function of α. In each chain, the overlap distribution is first smooth, but then develops a tiered structure, indicating that the solutions are found in well separated clusters. On chains of not too large instances, all remaining solutions are eventually observed to be found in only one small cluster before vanishing. This condensation transition point is estimated by finite size scaling to be αc = 4.26 with an apparent critical exponent of about 1.7. The average overlap value is also observed to increase with α up to the transition, indicating a reduction in solutions space size, in accordance with theoretical predictions. The solutions are generated by a local heuristic, ASAT, and compared to those found by the Survey Propagation algorithm up to αc.
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| 2. |
- Diaz-Mendez, Rogelio, et al.
(författare)
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Scaling of the magnetic permeability at the Berezinskii–Kosterlitz–Thouless transition from Coulomb gas simulations
- 2018
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Ingår i: Journal of Statistical Mechanics. - : IOP Publishing. - 1742-5468 .- 1742-5468. ; 2018:12
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Tidskriftsartikel (refereegranskat)abstract
- A new approach to the Berezinskii–Kosterlitz–Thouless transition in the two-dimensional Coulomb gas model is explored by Monte Carlo simulation and finite size scaling. The usual mapping of a neutral two-dimensional superconductor in zero magnetic field to a Coulomb gas leads to an unscreened logarithmic interaction between the vortices, and with periodic boundary conditions vortex configurations are always vorticity neutral with an equal number of plus and minus vortices. We demonstrate that relaxing the neutrality condition has certain advantages. It leads to non-neutral vortex configurations that can appear in real systems with open boundary conditions and permits calculation of the compressibility, which for thin film superconductors corresponds to the magnetic permeability. The vortex-number fluctuation has remarkable scaling properties at and below the Berezinskii–Kosterlitz–Thouless transition. The fugacity variable becomes dangerously irrelevant in the low-temperature phase and leads to a multiplicative scaling correction to the mean-square vortex-number fluctuation and to the magnetic permeability. This multiplicative correction strongly affects the scaling properties of the vorticity fluctuation at and below the transition. Consequences of these findings are demonstrated using Monte Carlo simulations. Inclusion of the next-higher order correction to scaling is found to play an important role in the analysis of numerical data for the vortex number fluctuation and permits accurate determination of the critical properties.
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| 3. |
- Pigeon, Simon, et al.
(författare)
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Tracer particle diffusion in a system with hardcore interacting particles
- 2017
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Ingår i: Journal of Statistical Mechanics: Theory and Experiment. - : IOP Publishing. - 1742-5468. ; 2017:12
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Tidskriftsartikel (refereegranskat)abstract
- In this study, inspired by the work of Nakazato and Kitahara (1980 Prog. Theor. Phys. 64 2261), we consider the theoretical problem of tracer particle diffusion in an environment of diffusing hardcore interacting crowder particles. The tracer particle has a different diffusion constant from the crowder particles. Based on a transformation of the generating function, we provide an exact formal expansion for the tracer particle probability density, valid for any lattice in the thermodynamic limit. By applying this formal solution to dynamics on a regular Bravais lattice we provide a closed form approximation for the tracer particle diffusion constant which extends the Nakazato and Kitahara results to include also b.c.c. and f.c.c. lattices. Finally, we compare our analytical results to simulations in two and three dimensions.
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| 4. |
- Innocenti, Nicolas, 1986-, et al.
(författare)
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Lognormality and oscillations in the coverage of high-throughput transcriptomic data towards gene ends
- 2013
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Ingår i: Journal of Statistical Mechanics. - : Institute of Physics (IOP). - 1742-5468 .- 1742-5468. ; 2013:10, s. P10013-
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Tidskriftsartikel (refereegranskat)abstract
- High-throughput transcriptomics experiments have reached the stage where the count of the number of reads alignable to a given position can be treated as an almost-continuous signal. This allows us to ask questions of biophysical/biotechnical nature, but which may still have biological implications. Here we show that when sequencing RNA fragments from one end, as is the case on most platforms, an oscillation in the read count is observed at the other end. We further show that these oscillations can be well described by Kolmogorov's 1941 broken stick model. We investigate how the model can be used to improve predictions of gene ends (3' transcript ends), but conclude that with present data the improvement is only marginal. The results highlight subtle effects in high-throughput transcriptomics experiments which do not have a biological origin, but which may still be used to obtain biological information.
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| 5. |
- Jia, Tao, 1983-, et al.
(författare)
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An empirical study on human mobility and its agent-based modeling
- 2012
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Ingår i: Journal of Statistical Mechanics. - Bristol : Institute of Physics Publishing (IOPP). - 1742-5468 .- 1742-5468.
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Tidskriftsartikel (refereegranskat)abstract
- This paper aims to analyze the GPS traces of 258 volunteers for a better understanding of both the human mobility patterns and the mechanism. We report the regular and scaling properties of human mobility from several aspects, and importantly we find its levy flight characteristic which is consistent with the previous studies. We further assume two factors that may govern the levy flight property: (1) the scaling and hierarchical properties of the purpose clusters which serve as the underlying spatial structure, and (2) the individual preferential behavior. To verify the assumptions, we implement an agent-based model with the two factors, and the simulated agents indeed reproduce the same levy flight pattern as the observed one. In order to enable the model to reproduce more mobility patterns, we add the model a third factor, the jumping factor which means the probability that one person may cancel the regular mobility schedule and visit a random place. With this factor, our model could cover a relatively wide range of human mobility patterns with exponent values from 1.55 to 2.05.
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| 6. |
- Penfold, R, et al.
(författare)
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A simple analysis of thermodynamic properties for classical plasmas: II. Validation
- 2005
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Ingår i: Journal of Statistical Mechanics: Theory and Experiment. - 1742-5468.
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Tidskriftsartikel (refereegranskat)abstract
- The generalized hole corrected Debye-Huckel theory (Penfold et al J. Stat. Mech. (2005) P06009) is implemented. Predictions of thermodynamic functions and simple structural properties compare favourably with results from closure of the Ornstein-Zernike integral equation in the mean spherical approximation, and with Monte Carlo simulation of the charged hard sphere primitive model. A strictly nonelectroneutral system was simulated using a conventional electrolyte program and the properties subsequently corrected for the configuration independent background terms. No convergence difficulties were encountered over the concentration range studied. With the new theory, activity coefficients of good accuracy can be obtained in a simple analytical form that is suitable for use with an approximate free energy density functional describing ion-ion correlations in screening atmospheres.
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| 7. |
- Rocha, Luis E C, 1981-
(författare)
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Structural evolution of the Brazilian airport network
- 2009
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Ingår i: Journal of Statistical Mechanics. - Bristol : Institute of Physics. - 1742-5468 .- 1742-5468. ; , s. 04020-
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Tidskriftsartikel (refereegranskat)abstract
- The aviation sector is profitable, but sensitive to economic fluctuations, geopolitical constraints and governmental regulations. As for other means of transportation, the relation between origin and destination results in a complex map of routes, which can be complemented with information associated with the routes themselves, for instance, frequency, traffic load and distance. The theory of networks provides a natural framework for investigating the dynamics on the resulting structure. Here, we investigate the structure and evolution of the Brazilian airport network (BAN) as regards several quantities: routes, connections, passengers and cargo. Some structural features are in accordance with previous results for other airport networks. The analysis of the evolution of the BAN shows that its structure is dynamic, with changes in the relative relevance of some airports and routes. The results indicate that the connections converge to specific routes. The network shrinks at the route level but grows in number of passengers and amount of cargo, which more than doubled during the period studied.
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| 8. |
- Rosengren, Hjalmar, 1972
(författare)
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Elliptic pfaffians and solvable lattice models
- 2016
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Ingår i: Journal of Statistical Mechanics: Theory and Experiment. - : IOP Publishing. - 1742-5468. ; 2016:8
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Tidskriftsartikel (refereegranskat)abstract
- We introduce and study twelve multivariable theta functions defined by pfaffians with elliptic function entries. We show that, when the crossing parameter is a cubic root of unity, the domain wall partition function for the eight-vertex-solid-on-solid model can be written as a sum of two of these pfaffians. As a limit case, we express the domain wall partition function for the three-colour model as a sum of two Hankel determinants. We also show that certain solutions of the TQ-equation for the supersymmetric eight-vertex model can be expressed in terms of elliptic pfaffians.
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| 9. |
- Velasco, Sergio, 1980
(författare)
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Non-equilibrium statistical mechanics: partition functions and steepest entropy increase
- 2011
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Ingår i: Journal of Statistical Mechanics: Theory and Experiment. - : IOP Publishing. - 1742-5468. ; 2011:5
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Tidskriftsartikel (refereegranskat)abstract
- On the basis of just the microscopic definition of thermodynamic entropy and the definition of the rate of entropy increase as the sum of products of thermodynamic fluxes and their conjugated forces, we have derived a general expression for non-equilibrium partition functions, which has the same form as the partition function previously obtained by other authors using different assumptions. Secondly we show that Onsager's reciprocity relations are equivalent to the assumption of steepest entropy ascent, independently of the choice of metric for the space of probability distributions. Finally we show that the Fisher-Rao metric for the space of probability distributions is the only one that guarantees that dissipative systems are what we call constantly describable (describable in terms of the same set of macroscopic observables during their entire trajectory of evolution towards equilibrium). The Fisher-Rao metric is fundamental to Beretta's dissipative quantum mechanics; therefore our last result provides a further justification for Beretta's theory.
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| 10. |
- Berg, Marcus, 1973-, et al.
(författare)
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Manifest modular invariance in the near-critical Ising model
- 2024
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Ingår i: Journal of Statistical Mechanics. - : Institute of Physics (IOP). - 1742-5468. ; 2024:1
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Tidskriftsartikel (refereegranskat)abstract
- Using recent results in mathematics, I point out that free energies and scale-dependent central charges away from criticality can be represented in compact form where modular invariance is manifest. The main example is the near-critical Ising model on a thermal torus, but the methods are not restricted to modular symmetry, and apply to automorphic symmetries more generally. One application is finite-size effects.
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