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Cisternas, J.; Mellado, P.; Urbina, F.; Portilla, C.; Carrasco, M.; Concha, A. |
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Title |
Stable and unstable trajectories in a dipolar chain |
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2021 |
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Physical Review B |
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Phys. Rev. B |
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103 |
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13 |
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134443 |
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MAGNETIC MONOPOLES; CRYSTAL STATISTICS; INTERFERENCE; HYSTERESIS; RELAXATION; ENTROPY |
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Abstract |
In classical mechanics, solutions can be classified according to their stability. Each of them is part of the possible trajectories of the system. However, the signatures of unstable solutions are hard to observe in an experiment, and most of the times if the experimental realization is adiabatic, they are considered just a nuisance. Here we use a small number of XY magnetic dipoles subject to an external magnetic field for studying the origin of their collective magnetic response. Using bifurcation theory we have found all the possible solutions being stable or unstable, and explored how those solutions are naturally connected by points where the symmetries of the system are lost or restored. Unstable solutions that reveal the symmetries of the system are found to be the culprit that shape hysteresis loops in this system. The complexity of the solutions for the nonlinear dynamics is analyzed using the concept of boundary basin entropy, finding that the damping timescale is critical for the emergence of fractal structures in the basins of attraction. Furthermore, we numerically found domain wall solutions that are the smallest possible realizations of transverse walls and vortex walls in magnetism. We experimentally confirmed their existence and stability showing that our system is a suitable platform to study domain wall dynamics at the macroscale. |
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2469-9950 |
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WOS:000646311300001 |
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UAI @ alexi.delcanto @ |
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1386 |
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Letelier, O.R.; Clautiaux, F.; Sadykov, R. |
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Title |
Bin Packing Problem with Time Lags |
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2022 |
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Informs Journal On Computing |
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INFORMS J. Comput. |
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Early Access |
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integer programming; algorithms; cutting planes; branch and bound; production-scheduling; cutting stock; relaxation |
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We introduce and motivate several variants of the bin packing problem where bins are assigned to time slots, and minimum and maximum lags are required between some pairs of items. We suggest two integer programming formulations for the general problem: a compact one and a stronger formulation with an exponential number of variables and constraints. We propose a branch-cut-and-price approach that exploits the latter formulation. For this purpose, we devise separation algorithms based on a mathematical characterization of feasible assignments for two important special cases of the problem: when the number of possible bins available at each period is infinite and when this number is limited to one and time lags are nonnegative. Computational experiments are reported for instances inspired from a real-case application of chemical treatment planning in vineyards, as well as for literature instances for special cases of the problem. The experimental results show the efficiency of our branch-cutand-price approach, as it outperforms the compact formulation on newly proposed instances and is able to obtain improved lower and upper bounds for literature instances. Summary of Contribution: The paper considers a new variant of the bin packing problem, which is one of the most important problems in operations research. A motivation for introducing this variant is given, as well as a real-life application. We present a novel and original exact branch-cut-and-price algorithm for the problem. We implement this algorithm, and we present the results of extensive computational experiments. The results show a very good performance of our algorithm. We give several research directions that can be followed by subsequent researchers to extend our contribution to more complex and generic problems. |
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1091-9856 |
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WOS:000804384300001 |
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UAI @ alexi.delcanto @ |
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1588 |
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Mellado, P. |
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Title |
Timescales in the thermal dynamics of magnetic dipolar clusters |
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2020 |
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Physical Review B |
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Phys. Rev. B |
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102 |
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21 |
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214442 |
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ARTIFICIAL SPIN ICE; RELAXATION; FRACTIONALIZATION; FRUSTRATION; GLASSES; PHYSICS; PHASE; MODEL |
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The collective behavior of thermally active structures offers clues on the emergent degrees of freedom and the physical mechanisms that determine the low-energy state of a variety of systems. Here, the thermally active dynamics of magnetic dipoles at square plaquettes is modeled in terms of Brownian oscillators in contact with a heat bath. Solution of the Langevin equation for a set of interacting x-y dipoles allows the identification of the timescales and correlation length that reveal how interactions, temperature, damping, and inertia may determine the frequency modes of edge and bulk magnetic mesospins in artificial dipolar systems. |
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UAI @ alexi.delcanto @ |
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1316 |
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