arXiv subjects
Publications and source records attributed to A. R. Lima.
We present a model to describe the collective motion of barchan dunes in a field. Our model is able to reproduce the observation that a typical dune stays confined within a stripe. We also obtain some of the pattern structures which ressemble those observed from aerial photos which we do analyse and compare with the specific field of Laâyounne.
In this letter we propose the use of physics techniques for entropy determination on constrained parameter optimization problems. The main feature of such techniques, the construction of an unbiased walk on energy space, suggests their use on the quest for optimal solutions of an optimization problem. Moreover, the entropy, and its associated density of states, give us information concerning the feasibility of solutions.
In this work we investigate the classical ferromagnetic XY-model in two dimensions subject to a symmetry breaking field which impose a $Z_2$ symmetry to the system. We used the broad histogram method combined with microcanonical simulations and finite-size scaling analysis to estimate the critical temperature and critical exponents of this system with little computational effort. In addition, we present a general procedure which makes possible to use the broad histogram method for continuous systems, also when the macroscopic quantities needed by the method cannot be obtained analytically. Our results are robust under the choice of four different pseudo-random number generators.
We follow the dynamic evolution of a cluster of Ising spins pointing up surrounded by other spins pointing down, on a lattice. The cluster represents a liquid drop. Under a microscopic point of view, the short range ferromagnetic coupling between these spins plays the role of the van der Waals attraction. Alternatively, under a macroscopic point of view, the same ferromagnetic coupling gives rise to the surface tension along the drop boundary. This naive model is applied to the study of different systems, out of thermodynamic equilibrium. For each such a system, other interaction terms can be included, for instance an external magnetic field with a downwards uniform gradient, representing Earth's gravity. Also, for each system, proper dynamic rules and boundary conditions are adopted. The behaviour of such a drop is monitored as a function of time, through computer simulations. Many quantities of interest, in particular those related to drop fragmentation, were measured and the results were compared with available experimental data. The real systems we have in mind are exemplified by water drops falling from a leaky faucet, nuclear multifragmentation, mercury drops falling on the ground, magnetic hysteresis curves, and interface roughness.
This is a reply to the comment by M. Kastner and M. Promberger [cond-mat/0011516] on the paper published in J. Stat. Phys. 99, 691 (2000) and also in cond-mat/0002176. We show that all their criticisms do not apply.
In this paper we apply the multicanonical method of statistical physics on the number-partitioning problem (NPP). This problem is a basic NP-hard problem from computer science, and can be formulated as a spin-glass problem. We compute the spectral degeneracy, which gives us information about the number of solutions for a given cost $E$ and cardinality $m$. We also study an extension of this problem for $Q$ partitions. We show that a fundamental difference on the spectral degeneracy of the generalized ($Q>2$) NPP exists, which could explain why it is so difficult to find good solutions for this case. The information obtained with the multicanonical method can be very useful on the construction of new algorithms.
We discuss the conceptual differences between the Broad Histogram (BHM) and reweighting methods in general, and particularly the so-called Multicanonical (MUCA) approaches. The main difference is that BHM is based on microcanonical, fixed-energy averages which depends only on the good statistics taken {\bf inside} each energy level. The detailed distribution of visits among different energy levels, determined by the particular dynamic rule one adopts, is irrelevant. Contrary to MUCA, where the results are extracted from the dynamic rule itself, within BHM any microcanonical dynamics could be adopted. As a numerical test, we have used both BHM and MUCA in order to obtain the spectral energy degeneracy of the Ising model in $4 \times 4 \times 4$ and $32 \times 32$ lattices, for which exact results are known. We discuss why BHM gives more accurate results than MUCA, even using {\bf the same} Markovian sequence of states. In addition, such advantage increases for larger systems.
We extended the Broad Histogram Method in order to obtain spectral degeneracies for systems with multiparametric Hamiltonians. As examples we obtained the critical lines for the square lattice Ising model with nearest and next-nearest neighbor interactions and the antiferromagnetic Ising model in an external field. For each system, the entire critical line is obtained using data from a single computer run. We also discuss the accuracy and efficiency of our method.
With the purpose of explaining recent experimental findings, we study the distribution $A(λ)$ of distances $λ$ traversed by a block that slides on an inclined plane and stops due to friction. A simple model in which the friction coefficient $μ$ is a random function of position is considered. The problem of finding $A(λ)$ is equivalent to a First-Passage-Time problem for a one-dimensional random walk with nonzero drift, whose exact solution is well-known. From the exact solution of this problem we conclude that: a) for inclination angles $θ$ less than $θ_c=\tan(\avμ)$ the average traversed distance $\avλ$ is finite, and diverges when $θ\to θ_c^{-}$ as $\avλ \sim (θ_c-θ)^{-1}$; b) at the critical angle a power-law distribution of slidings is obtained: $A(λ) \sim λ^{-3/2}$. Our analytical results are confirmed by numerical simulation, and are in partial agreement with the reported experimental results. We discuss the possible reasons for the remaining discrepancies.
We apply the Broad Histogram Method to an Ising system in the context of the recently reformulated Generalized Thermostatistics, and we claim it to be a very efficient simulation tool for this non-extensive statistics. Results are obtained for the nearest-neighbour version of the Ising model for a range of values of the $q$ parameter of Generalized Thermostatistics. We found an evidence that the 2D-Ising model does not undergo phase transitions at finite temperatures except for the extensive case $q=1$.
We present a study of both the ``Iterative Procedure'' and the ``$β\to β'$ transformation'', proposed by Tsallis et al (Physica A261, 534) to find the probabilities $p_i$ of a system to be in a state with energy $ε_i$, within the framework of a generalized statistical mechanics. Using stability and convexity arguments, we argue that the iterative procedure does not always provide the right temperature dependence of thermodynamic observables. In addition, we show how to get the correct answers from the ``$β\to β'$ transformation''. Our results provide an evidence that the Tsallis statistics with normalized q-expectation values is stable for all ranges of temperatures. We also show that the cut-off in the computation of probabilities is required to achieve the stable solutions.