The Experts below are selected from a list of 57246 Experts worldwide ranked by ideXlab platform
A Robledo - One of the best experts on this subject based on the ideXlab platform.
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logistic map trajectory distributions renormalization group entropy and criticality at the transition to chaos
Chaos, 2021Co-Authors: Alvaro Diazruelas, Fulvio Baldovin, A RobledoAbstract:We study the evolution of the probability density of ensembles of iterates of the logistic map that advance toward and finally remain at attractors of representative dynamical regimes. We consider the mirror families of superstable attractors along the period-doubling cascade and of chaotic-band attractors along the inverse band-splitting cascade. We examine also their common aperiodic accumulation point. The Iteration Time progress of the densities of trajectories is determined via the action of the Frobenius–Perron (FP) operator. As a difference with the study of individual orbits, the analysis of ensembles of positions offers a viewpoint from which the nonlinear dynamical features of this iconic model can be better characterized in statistical-mechanical terms. The scaling of densities along the considered families of attractors conforms to a renormalization-group (RG) structure, while their entropies are seen to attain extrema at the fixed points of the RG flows. Additionally, this entropy as a function of the map control parameter displays the characteristic features of an equation of state of a thermal system undergoing a second-order phase transition. We discuss our results.
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logistic map trajectory distributions renormalization group entropy and criticality at the transition to chaos
arXiv: Statistical Mechanics, 2021Co-Authors: Alvaro Diazruelas, Fulvio Baldovin, A RobledoAbstract:We study the evolution of the probability density of ensembles of iterates of the logistic map that advance towards and finally remain at attractors of representative dynamical regimes. We consider the mirror families of superstable attractors along the period-doubling cascade, and of chaotic-band attractors along the inverse band-splitting cascade. We examine also their common aperiodic accumulation point. The Iteration Time progress of the densities of trajectories is determined via the action of the Frobenius-Perron (FP) operator. As a difference with the study of individual orbits, the analysis of ensembles of positions offers a viewpoint from which the nonlinear dynamical features of this iconic model can be better characterized in statistical-mechanical terms. The scaling of the densities along the considered families of attractors conforms to a renormalization-group (RG) structure, while their entropies are seen to attain extrema at the fixed points of the RG flows. Additionally, this entropy as a function of the map control parameter displays the characteristic features of an equation of state of a thermal system undergoing a second-order phase transition. We discuss our results.
Alvaro Diazruelas - One of the best experts on this subject based on the ideXlab platform.
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logistic map trajectory distributions renormalization group entropy and criticality at the transition to chaos
Chaos, 2021Co-Authors: Alvaro Diazruelas, Fulvio Baldovin, A RobledoAbstract:We study the evolution of the probability density of ensembles of iterates of the logistic map that advance toward and finally remain at attractors of representative dynamical regimes. We consider the mirror families of superstable attractors along the period-doubling cascade and of chaotic-band attractors along the inverse band-splitting cascade. We examine also their common aperiodic accumulation point. The Iteration Time progress of the densities of trajectories is determined via the action of the Frobenius–Perron (FP) operator. As a difference with the study of individual orbits, the analysis of ensembles of positions offers a viewpoint from which the nonlinear dynamical features of this iconic model can be better characterized in statistical-mechanical terms. The scaling of densities along the considered families of attractors conforms to a renormalization-group (RG) structure, while their entropies are seen to attain extrema at the fixed points of the RG flows. Additionally, this entropy as a function of the map control parameter displays the characteristic features of an equation of state of a thermal system undergoing a second-order phase transition. We discuss our results.
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logistic map trajectory distributions renormalization group entropy and criticality at the transition to chaos
arXiv: Statistical Mechanics, 2021Co-Authors: Alvaro Diazruelas, Fulvio Baldovin, A RobledoAbstract:We study the evolution of the probability density of ensembles of iterates of the logistic map that advance towards and finally remain at attractors of representative dynamical regimes. We consider the mirror families of superstable attractors along the period-doubling cascade, and of chaotic-band attractors along the inverse band-splitting cascade. We examine also their common aperiodic accumulation point. The Iteration Time progress of the densities of trajectories is determined via the action of the Frobenius-Perron (FP) operator. As a difference with the study of individual orbits, the analysis of ensembles of positions offers a viewpoint from which the nonlinear dynamical features of this iconic model can be better characterized in statistical-mechanical terms. The scaling of the densities along the considered families of attractors conforms to a renormalization-group (RG) structure, while their entropies are seen to attain extrema at the fixed points of the RG flows. Additionally, this entropy as a function of the map control parameter displays the characteristic features of an equation of state of a thermal system undergoing a second-order phase transition. We discuss our results.
Ifan G Hughes - One of the best experts on this subject based on the ideXlab platform.
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the raspberry pi auto aligner machine learning for automated alignment of laser beams
arXiv: Instrumentation and Detectors, 2020Co-Authors: Renju S Mathew, Roshan Odonnell, Danielle Pizzey, Ifan G HughesAbstract:We present a novel solution to automated beam alignment optimization. This device is based on a Raspberry Pi computer, stepper motors, commercial optomechanics and electronic devices, and the open source machine learning algorithm M-LOOP. We provide schematic drawings for the custom hardware necessary to operate the device and discuss diagnostic techniques to determine the performance. The beam auto-aligning device has been used to improve the alignment of a laser beam into a single-mode optical fiber from manually optimized fiber alignment with an Iteration Time of typically 20~minutes. We present example data of one such measurement to illustrate device performance.
Hughes, Ifan G. - One of the best experts on this subject based on the ideXlab platform.
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The Raspberry Pi Auto-aligner: Machine Learning for Automated Alignment of Laser Beams
'AIP Publishing', 2020Co-Authors: Mathew, Renju S., O'donnell Roshan, Pizzey Danielle, Hughes, Ifan G.Abstract:We present a novel solution to automated beam alignment optimization. This device is based on a Raspberry Pi computer, stepper motors, commercial optomechanics and electronic devices, and the open source machine learning algorithm M-LOOP. We provide schematic drawings for the custom hardware necessary to operate the device and discuss diagnostic techniques to determine the performance. The beam auto-aligning device has been used to improve the alignment of a laser beam into a single-mode optical fiber from manually optimized fiber alignment with an Iteration Time of typically 20~minutes. We present example data of one such measurement to illustrate device performance.Comment: 8 pages, 4 figure
Fulvio Baldovin - One of the best experts on this subject based on the ideXlab platform.
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logistic map trajectory distributions renormalization group entropy and criticality at the transition to chaos
Chaos, 2021Co-Authors: Alvaro Diazruelas, Fulvio Baldovin, A RobledoAbstract:We study the evolution of the probability density of ensembles of iterates of the logistic map that advance toward and finally remain at attractors of representative dynamical regimes. We consider the mirror families of superstable attractors along the period-doubling cascade and of chaotic-band attractors along the inverse band-splitting cascade. We examine also their common aperiodic accumulation point. The Iteration Time progress of the densities of trajectories is determined via the action of the Frobenius–Perron (FP) operator. As a difference with the study of individual orbits, the analysis of ensembles of positions offers a viewpoint from which the nonlinear dynamical features of this iconic model can be better characterized in statistical-mechanical terms. The scaling of densities along the considered families of attractors conforms to a renormalization-group (RG) structure, while their entropies are seen to attain extrema at the fixed points of the RG flows. Additionally, this entropy as a function of the map control parameter displays the characteristic features of an equation of state of a thermal system undergoing a second-order phase transition. We discuss our results.
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logistic map trajectory distributions renormalization group entropy and criticality at the transition to chaos
arXiv: Statistical Mechanics, 2021Co-Authors: Alvaro Diazruelas, Fulvio Baldovin, A RobledoAbstract:We study the evolution of the probability density of ensembles of iterates of the logistic map that advance towards and finally remain at attractors of representative dynamical regimes. We consider the mirror families of superstable attractors along the period-doubling cascade, and of chaotic-band attractors along the inverse band-splitting cascade. We examine also their common aperiodic accumulation point. The Iteration Time progress of the densities of trajectories is determined via the action of the Frobenius-Perron (FP) operator. As a difference with the study of individual orbits, the analysis of ensembles of positions offers a viewpoint from which the nonlinear dynamical features of this iconic model can be better characterized in statistical-mechanical terms. The scaling of the densities along the considered families of attractors conforms to a renormalization-group (RG) structure, while their entropies are seen to attain extrema at the fixed points of the RG flows. Additionally, this entropy as a function of the map control parameter displays the characteristic features of an equation of state of a thermal system undergoing a second-order phase transition. We discuss our results.
