Chaotic diffusion of orbits in systems with divided phase space

In this paper we discuss the relevance of diffusive processes in multidimensional Hamiltonian systems. By means of a rather simple model, we present evidence that for moderate-to-strong chaotic systems the stochastic motion remains confined to disjoint domains on the energy surface, at least for mild motion times. We show that only for extremely large timescales and for rather large perturbations, does the chaotic component appear almost fully connected through the relics of the resonance structure. The discussion whether diffusion over the energy surface could actually occur in asteroidal or galaxy dynamics is also included.Fil: Giordano, Claudia Marcela. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto de Astrofísica La Plata. Universidad Nacional de La Plata. Facultad de Ciencias Astronómicas y Geofísicas. Instituto de Astrofísica La Plata; ArgentinaFil: Cincotta, Pablo Miguel. Universidad Nacional de La Plata. Facultad de Ciencias Astronómicas y Geofísicas; Argentin

Household food waste from an international perspective

open2noThe food waste debate has flourished during the last years, leading to an impressive increase in the number of scientific publications. After FAO stated that about one-third of the total food produced at the global level goes wasted, the topic has been given increasing attention, and it became a specific sub-goal of the SDG 12 of Agenda 2030. The most recent study published by UNEP reported that globally around 931 million tons of food waste was generated in 2019, 61% of which came from households.openGiordano, C; Franco, S.Giordano, C; Franco, S

Stochastic approach to diffusion inside the chaotic layer of a resonance

We model chaotic diffusion, in a symplectic 4D map by using the result of a theorem that was developed for stochastically perturbed integrable Hamiltonian systems. We explicitly consider a map defined by a free rotator (FR) coupled to a standard map (SM). We focus in the diffusion process in the action, $I$, of the FR, obtaining a semi--numerical method to compute the diffusion coefficient. We study two cases corresponding to a thick and a thin chaotic layer in the SM phase space and we discuss a related conjecture stated in the past. In the first case the numerically computed probability density function for the action $I$ is well interpolated by the solution of a Fokker-Planck (F-P) equation, whereas it presents a non--constant time delay respect to the concomitant F-P solution in the second case suggesting the presence of an anomalous diffusion time scale. The explicit calculation of a diffusion coefficient for a 4D symplectic map can be useful to understand the slow diffusion observed in Celestial Mechanics and Accelerator Physics.Comment: This is the author's version of a work that was submitted to Physical Review E (http://pre.aps.org

Chirikov and Nekhoroshev diffusion estimates: bridging the two sides of the river

We present theoretical and numerical results pointing towards a strong connection between the estimates for the diffusion rate along simple resonances in multidimensional nonlinear Hamiltonian systems that can be obtained using the heuristic theory of Chirikov and a more formal one due to Nekhoroshev. We show that, despite a wide-spread impression, the two theories are complementary rather than antagonist. Indeed, although Chirikov's 1979 review has thousands of citations, almost all of them refer to topics such as the resonance overlap criterion, fast diffusion, the Standard or Whisker Map, and not to the constructive theory providing a formula to measure diffusion along a single resonance. However, as will be demonstrated explicitly below, Chirikov's formula provides values of the diffusion coefficient which are quite well comparable to the numerically computed ones, provided that it is implemented on the so-called optimal normal form derived as in the analytic part of Nekhoroshev's theorem. On the other hand, Chirikov's formula yields unrealistic values of the diffusion coefficient, in particular for very small values of the perturbation, when used in the original Hamiltonian instead of the optimal normal form. In the present paper, we take advantage of this complementarity in order to obtain accurate theoretical predictions for the local value of the diffusion coefficient along a resonance in a specific 3DoF nearly integrable Hamiltonian system. Besides, we compute numerically the diffusion coefficient and a full comparison of all estimates is made for ten values of the perturbation parameter, showing a very satisfactory agreement.Comment: 25 pages, 9 figures. NOTICE: this is the author's version of a work that was accepted for publication in Physica D. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publicatio

Sodium hydroxide pretreatment as an effective approach to reduce the dye/holes recombination reaction in P-Type DSCs

We report the synthesis of a novel squaraine dye (VG21-C12) and investigate its behavior as p-type sensitizer for p-type Dye-Sensitized Solar Cells. The results are compared with O4-C12, a well-known sensitizer for p-DSC, and sodium hydroxide pretreatment is described as an effective approach to reduce the dye/holes recombination. Various variable investigation such as dipping time, dye loading, photocurrent, and resulting cell efficiency are also reported. Electrochemical impedance spectroscopy (EIS) was utilized for investigating charge transport properties of the different photoelectrodes and the recombination phenomena that occur at the (un)modified electrode/electrolyte interface

Phase correlations in chaotic dynamics: a Shannon entropy measure

In the present work, we investigate phase correlations by recourse to the Shannon entropy. Using theoretical arguments, we show that the entropy provides an accurate measure of phase correlations in any dynamical system, in particular when dealing with a chaotic diffusion process. We apply this approach to different low-dimensional maps in order to show that indeed the entropy is very sensitive to the presence of correlations among the successive values of angular variables, even when it is weak. Later on, we apply this approach to unveil strong correlations in the time evolution of the phases involved in the Arnold’s Hamiltonian that lead to anomalous diffusion, particularly when the perturbation parameters are comparatively large. The obtained results allow us to discuss the validity of several approximations and assumptions usually introduced to derive a local diffusion coefficient in multidimensional near-integrable Hamiltonian systems, in particular the so-called reduced stochasticity approximation.Instituto de Astrofísica de La Plat

Chaotic diffusion of orbits in systems with divided phase space

In this paper we discuss the relevance of diffusive processes in multidimensional Hamiltonian systems. By means of a rather simple model, we present evidence that for moderate-to-strong chaotic systems the stochastic motion remains confined to disjoint domains on the energy surface, at least for mild motion times. We show that only for extremely large timescales and for rather large perturbations, does the chaotic component appear almost fully connected through the relics of the resonance structure. The discussion whether diffusion over the energy surface could actually occur in asteroidal or galaxy dynamics is also included.Facultad de Ciencias Astronómicas y Geofísica

Phase correlations in chaotic dynamics: a Shannon entropy measure

In the present work, we investigate phase correlations by recourse to the Shannon entropy. Using theoretical arguments, we show that the entropy provides an accurate measure of phase correlations in any dynamical system, in particular when dealing with a chaotic diffusion process. We apply this approach to different low-dimensional maps in order to show that indeed the entropy is very sensitive to the presence of correlations among the successive values of angular variables, even when it is weak. Later on, we apply this approach to unveil strong correlations in the time evolution of the phases involved in the Arnold’s Hamiltonian that lead to anomalous diffusion, particularly when the perturbation parameters are comparatively large. The obtained results allow us to discuss the validity of several approximations and assumptions usually introduced to derive a local diffusion coefficient in multidimensional near-integrable Hamiltonian systems, in particular the so-called reduced stochasticity approximation.Instituto de Astrofísica de La Plat