共查询到20条相似文献,搜索用时 9 毫秒
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Niloufar Faghihi Simiso Mkhonta Ken R. Elder Martin Grant 《The European Physical Journal B - Condensed Matter and Complex Systems》2018,91(3):55
Using a minimal model based on the phase-field-crystal formalism, we study the coupling between the density and magnetization in ferromagnetic solids. Analytical calculations for the square phase in two dimensions are presented and the small deformation properties of the system are examined. Furthermore, numerical simulations are conducted to study the influence of an external magnetic field on various phase transitions, the anisotropic properties of the free energy functional, and the scaling behaviour of the growth of the magnetic domains in a crystalline solid. It is shown that the energy of the system can depend on the direction of the magnetic moments, with respect to the crystalline direction. Furthermore, the growth of the magnetic domains in a crystalline solid is studied and is shown that the growth of domains is in agreement with expected behaviour. 相似文献
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S. Vaienti 《Journal of statistical physics》1989,56(3-4):403-413
For the Axiom-A attractors a relation is given between the topological pressure and the spectrum of the generalized Lyapunov exponents. As a consequence, a simple formula is found to compute the topological entropy of the attractor by means of a time series. The results are used to compute the large deviations for positive Lyapunov exponents. 相似文献
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In this Letter, the ordered and disordered regions of the field variable of an oscillator chain are studied. For this purpose, the mean Lyapunov exponent (MLE) theory is applied to the helicoidal Peyrard-Bishop (hPB) model. Applying mean Lyapunov exponent theory introduced by Shibata [H. Shibata, Physica A 264 (1999) 226] on the model shows that, the system is very sensitive to the potential parameters. By analyzing the behavior of the MLE with respect to the harmonic helicoidal coupling (K), it can be found that, it is not possible to set the Morse potential parameters of the hPB model in good qualitative agreement with other experimental and theoretical studies. Furthermore, the results show that the MLE is independent of length of the DNA chain. This achievement is important since it can be used to overcome the computational difficulties. 相似文献
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We study the largest Liapunov exponent for products of random matrices. The two classes of matrices considered are discrete,d-dimensional Laplacians, with random entries, and symplectic matrices that arise in the study ofd-dimensional lattices of coupled, nonlinear oscillators. We derive bounds on this exponent for all dimensions,d, and we show that ifd3, and the randomness is not too strong, one can obtain an explicit formula for the largest exponent in the thermodynamic limit. Our method is based on an equivalence between this problem and the problem of directed polymers in a random environment. 相似文献
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We consider the usual one-dimensional tight-binding Anderson model with the random potential taking only two values, 0 and, with probabilityp and 1–p, 0<p<1. We show that the Liapunov exponent
(E), E R. diverges as uniformly in the energyE. Using a result of Carmona, Klein, and Martinelli, this proves that for large enough, the integrated density of states is singular continuous. We also compute explicitly the exact asymptotics for a dense set of energies and we compare the results with numerical simulations. 相似文献
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Shingyu Leung 《Journal of computational physics》2011,230(9):3500-3524
We propose efficient Eulerian methods for approximating the finite-time Lyapunov exponent (FTLE). The idea is to compute the related flow map using the Level Set Method and the Liouville equation. There are several advantages of the proposed approach. Unlike the usual Lagrangian-type computations, the resulting method requires the velocity field defined only at discrete locations. No interpolation of the velocity field is needed. Also, the method automatically stops a particle trajectory in the case when the ray hits the boundary of the computational domain. The computational complexity of the algorithm is O(Δx?(d+1)) with d the dimension of the physical space. Since there are the same number of mesh points in the x–t space, the computational complexity of the proposed Eulerian approach is optimal in the sense that each grid point is visited for only O(1) time. We also extend the algorithm to compute the FTLE on a co-dimension one manifold. The resulting algorithm does not require computation on any local coordinate system and is simple to implement even for an evolving manifold. 相似文献
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The end-to-end distance and the contour length of single polymers in dynamic adsorbate layers were measured with a mechanical approach. Individual polysaccharide chains were covalently pinned to the surface with one segment and picked up randomly with an atomic force microscope tip. The polymer section between pinpoint and the pickup point was stretched by retracting the tip from the surface. The pinpoint was derived by measuring the normal force while laterally scanning the surface at constant height. For carboxy-methyl-amylose, a Kuhn length of 0.44 nm and a scaling exponent of 0.74 were found. 相似文献
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V. A. Golovko 《Russian Physics Journal》1979,22(2):165-169
A method of solving the Vlasov equation is developed for a crystal using an asymptotic expansion in terms of the temperature. The internal and free energy of cubic crystals is calculated with an accuracy up to terms proportional to T4.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 2, pp. 67–72, February, 1979. 相似文献
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E. Momoniat 《Physica A》2008,387(11):2427-2432
We consider a linear constant coefficient diffusion equation with a mixed derivative term that exhibits the same statistical properties as the phenomenological diffusion equation. The solution of this diffusion equation represents the time evolution of a probability distribution with oscillating tails. 相似文献
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Clarification of critical wetting with short-range forces by simulations has been hampered by the lack of accurate methods to locate where the transition occurs. We solve this problem by developing an anisotropic finite-size scaling approach and show that then the wetting transition is a "bulk" critical phenomenon with order parameter exponent equal to zero. For the Ising model in two dimensions, known exact results are straightforwardly reproduced. In three dimensions, it is shown that previous estimates for the location of the transition need revision, but the conclusions about a slow crossover away from mean-field behavior remain unaltered. 相似文献
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M. J. Sánchez-Granero M. Fernández-Martínez J. E. Trinidad-Segovia 《The European Physical Journal B - Condensed Matter and Complex Systems》2012,85(3):86
In this paper, three new algorithms are introduced in order to explore long memory in
financial time series. They are based on a new concept of fractal dimension of a curve. A
mathematical support is provided for each algorithm and its accuracy is tested for
different length time series by Monte Carlo simulations. In particular, in the case of
short length series, the introduced algorithms perform much better than the classical
methods. Finally, an empirical application for some stock market indexes as well as some
individual stocks is presented. 相似文献
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M. J. Sánchez-Granero M. Fernández-Martínez J. E. Trinidad-Segovia 《The European Physical Journal B - Condensed Matter and Complex Systems》2012,85(3):1-13
In this paper, three new algorithms are introduced in order to explore long memory in financial time series. They are based on a new concept of fractal dimension of a curve. A mathematical support is provided for each algorithm and its accuracy is tested for different length time series by Monte Carlo simulations. In particular, in the case of short length series, the introduced algorithms perform much better than the classical methods. Finally, an empirical application for some stock market indexes as well as some individual stocks is presented. 相似文献
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Geometric method-based procedures, which will be called GM algorithms herein, were introduced in [M.A. Sánchez Granero, J.E. Trinidad Segovia, J. García Pérez, Some comments on Hurst exponent and the long memory processes on capital markets, Phys. A 387 (2008) 5543-5551], to efficiently calculate the self-similarity exponent of a time series. In that paper, the authors showed empirically that these algorithms, based on a geometrical approach, are more accurate than the classical algorithms, especially with short length time series. The authors checked that GM algorithms are good when working with (fractional) Brownian motions. Moreover, in [J.E. Trinidad Segovia, M. Fernández-Martínez, M.A. Sánchez-Granero, A note on geometric method-based procedures to calculate the Hurst exponent, Phys. A 391 (2012) 2209-2214], a mathematical background for the validity of such procedures to estimate the self-similarity index of any random process with stationary and self-affine increments was provided. In particular, they proved theoretically that GM algorithms are also valid to explore long-memory in (fractional) Lévy stable motions. 相似文献
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《Nuclear Physics B》1998,528(3):533-552
We have extended the enumeration of self-avoiding walks on the Manhattan lattice from 28 to 53 steps and for self-avoiding polygons from 48 to 84 steps. Analysis of this data suggests that the walk generating function exponent γ = 1.3385 ± 0.003, which is different from the corresponding exponent on the square, triangular and honeycomb lattices. This provides numerical support for an argument recently advanced by Cardy, to the effect that excluding walks with parallel nearest-neighbour steps should cause a change in the exponent γ. The lattice topology of the Manhattan lattice precludes such parallel steps. 相似文献