Robust Convergence in Pulse-Coupled Oscillators with Delays

Nishimura, Joel; Friedman, Eric

doi:10.1103/physrevlett.106.194101

Cited by 77 publications

(123 citation statements)

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Section: Introductionmentioning

confidence: 99%

“…The half-lives of 77,78 Ni were measured for the first time by Hosmer et al [16], at NSCL, MSU. Recently the beta decay half-lives of 38 very neutron-rich Kr to Tc isotopes are measured at RIKEN [17].Despite the progress in the experimental side, we need theoretical estimates for half-lives of neutron rich nuclei, especially those belonging to the island of inversion. These calculations are based on allowed GT-transitions.…”

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confidence: 99%

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Nuclearβ⁻-decay half-lives for ${fp}$ and ${fpg}$ shell nuclei

Kumar

Srivastava

2016

J. Phys. G: Nucl. Part. Phys.

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Abstract. In the present work we calculate the allowed β − -decay half-lives of nuclei with Z = 20 − 30 and N ≤ 50 systematically under the framework of the nuclear shell model. A recent study shows that some nuclei in this region belong to the island of inversion. We perform calculation for f p shell nuclei using KB3G effective interaction. In the case of Ni, Cu, and Zn, we used JUN45 effective interaction. Theoretical results of Q values, half-lives, excitation energies, logf t values, and branching fractions are discussed and compared with the experimental data. In the Ni region, we also compared our calculated results with recent experimental data [Z. Y. Xu et al., Phys. Rev. Lett. 113, 032505, 2014]. Present results agree with the experimental data of half-lives in comparison to QRPA. Nuclear β − -decay half-lives for f p and f pg shell nuclei 2 IntroductionThe neutron density becomes very diffused and the single-particle spectrum shows the similarity of the harmonic-oscillator as we approach towards the neutron-drip line [1,2]. We can see this effect at N = 40 shell gap. Recently intruder configurations are found in the neutron rich nuclei around this shell gap [3,4,5,6,7]. Thus the nuclear structure study of these nuclei in this region is very important [8,9,10].Sorlin et al. Using RIBF facility at RIKEN, the half-lives of twenty neutron-rich nuclei with Z = 27 − 30 are reported in ref. [14]. In that work, sizable magicity was reported for both the proton number Z = 28 and the neutron number N = 50 in 78 Ni. A sudden shortening of half-lives of the nickel isotopes beyond N = 50 were observed in this work, although this effect is not found in the Cu-Ge-Ga chains. The half-lives results from LISE2000 spectrometer at GANIL for 71 Co and 73 Co are reported in ref.[15]. The half-lives of 77,78 Ni were measured for the first time by Hosmer et al. [16], at NSCL, MSU. Recently the beta decay half-lives of 38 very neutron-rich Kr to Tc isotopes are measured at RIKEN [17].Despite the progress in the experimental side, we need theoretical estimates for half-lives of neutron rich nuclei, especially those belonging to the island of inversion. These calculations are based on allowed GT-transitions. Many theoretical calculations from the quasiparticle random phase approximation (QRPA) based on the HartreeFock Bogoliubov theory [18] or other global models [19,20,21] are available in the literature. These calculations underestimate the correlation among nucleons which predict GT-strength at low-energies. Recently, shell model calculations for the β − -decays of Z = 9 − 13 nuclei are reported by Li and Ren [22]. The motivation of the present work is to study β − -decay properties of Z = 20 − 30 nuclei using the nuclear shell model. This paper is organized as follows. In section 2, we present the formulas for the calculation of β − decay half-lives. Shell model spaces, effective interactions and the quenching factors adopted in our calculations are reported in section 3. In section 4, we present theoretical results along w...

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Section: Introductionmentioning

confidence: 99%

mentioning

confidence: 99%

Nuclearβ⁻-decay half-lives for ${fp}$ and ${fpg}$ shell nuclei

Kumar

Srivastava

2016

J. Phys. G: Nucl. Part. Phys.

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“…Recent lifetime measurements on very n-rich nuclei nearby the A ∼ 130 waiting-point [12] show an overestimation of a factor of two or more of the half-life calculations based on the FRDM+QRPA approach. Also the scarce data available approaching the N = 126 shell closure [13] indicate an overestimation of the lifetimes predicted by the same model, in this case of more than one order of magnitude.…”

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confidence: 99%

First measurement of beta decay half-lives in neutron-rich Tl and Bi isotopes

et al. 2012

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Neutron-rich isotopes around lead, beyond N=126, have been studied exploiting the fragmentation of an uranium primary beam at the FRS-RISING setup at GSI. For the first time β-decay half-lives of 219 Bi and 211,212,213 Tl isotopes have been derived. The half-lives have been extracted using a numerical simulation developed for experiments in high-background conditions. Comparison with state of the art models used in r-process calculations is given, showing a systematic underestimation of the experimental values, at variance from close-lying nuclei.

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“…Furthermore, we provide rigorous lower bounds that guarantee the performance of this computational analytic approach and display how the probability of synchrony converges to 1 in highly connected graphs. This result is of biological relevance to the situations where synchrony is brought about via Type II PRCs, and is a useful guide for the construction of PCOs in sensor nets.Previous work found that a class of Type II PRC, denoted "Stong Type II" or "STII" (described later), could consistently converge to synchrony on fairly complex graphs with time delays [15]. This convergence was explained by showing that these PCOs would converge to synchrony if their phases were inside a critical range ρ 0 , essentially showing an l ∞ ball of stability.…”

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confidence: 99%

“…Previous work found that a class of Type II PRC, denoted "Stong Type II" or "STII" (described later), could consistently converge to synchrony on fairly complex graphs with time delays [15]. This convergence was explained by showing that these PCOs would converge to synchrony if their phases were inside a critical range ρ 0 , essentially showing an l ∞ ball of stability.…”

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confidence: 99%

Probabilistic convergence guarantees for type-II pulse-coupled oscillators

Nishimura

Friedman

2012

Phys. Rev. E

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We show that a large class of pulse coupled oscillators converge with high probability from random initial conditions on a large class of graphs with time delays. Our analysis combines previous local convergence results, probabilistic network analysis, and a new classification scheme for Type II phase response curves to produce rigorous lower bounds for convergence probabilities based on network density. These bounds are then used to develop a simple, fast and rigorous computational analytic technique. These results suggest new methods for the analysis of pulse coupled oscillators, and provide new insights into the operation of biological Type II phase response curves and also the design of decentralized and minimal clock synchronization schemes in sensor nets.Synchrony in systems of pulse-coupled oscillators (PCOs) is an important feature in physics, biology and engineering. Synchronization can range from being a pathological breakdown, as in epilepsy [1] to one of vital importance, such as in the proper functioning of the heart's sinoatrial node [2,3], to a framework to understand complex systems [4,5]. Additionally, there are attempts to utilize the simplicity of PCO synchronization to synchronize wireless sensor networks [6][7][8][9]. However, many of the idealized models inspired by synchronization are not able to synchronize when the system has a complicated graph structure and time delays -aspects expected in real physical systems. In order to deal with these issues, previous studies have considered oscillators augmented with memory [7,10], infinite spatial density [10] or indegree normalization [5,10]. While these studies have shown linear stability [5], or other forms of local convergence [7,10], global convergence in these settings has either been shown to be impossible [5] or remains unknown.Alternatively, a class of oscillators with Type II phase response curves (PRCs), have been connected to synchronizing behavior theoretically [11,12] and in nature [2,13,14]. The distinguishing feature of oscillators with Type II PRCs is that an oscillator's phase can either be decreased (inhibited) or increased (excited), depending on the internal state of the oscillator. In this paper we focus on PCOs with a particular class of type II phase response curves, introduced in our previous paper [15], which resembles those in nature [2,13] and are well suited for handling complex topologies and time delay. We also show how leveraging the main theorem from [15] allows for a computational analytic routine yielding a fast and rigorous estimate of the convergence probability of a system of PCOs. Furthermore, we provide rigorous lower bounds that guarantee the performance of this computational analytic approach and display how the probability of synchrony converges to 1 in highly connected graphs. This result is of biological relevance to the situations where synchrony is brought about via Type II PRCs, and is a useful guide for the construction of PCOs in sensor nets.Previous work found that a class of Type II PRC, denote...

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Robust Convergence in Pulse-Coupled Oscillators with Delays

Cited by 77 publications

References 20 publications

Nuclearβ⁻-decay half-lives for ${fp}$ and ${fpg}$ shell nuclei

Nuclearβ⁻-decay half-lives for ${fp}$ and ${fpg}$ shell nuclei

First measurement of beta decay half-lives in neutron-rich Tl and Bi isotopes

Probabilistic convergence guarantees for type-II pulse-coupled oscillators

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Robust Convergence in Pulse-Coupled Oscillators with Delays

Cited by 77 publications

References 20 publications

Nuclearβ−-decay half-lives for ${fp}$ and ${fpg}$ shell nuclei

Nuclearβ−-decay half-lives for ${fp}$ and ${fpg}$ shell nuclei

First measurement of beta decay half-lives in neutron-rich Tl and Bi isotopes

Probabilistic convergence guarantees for type-II pulse-coupled oscillators

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Nuclearβ⁻-decay half-lives for ${fp}$ and ${fpg}$ shell nuclei

Nuclearβ⁻-decay half-lives for ${fp}$ and ${fpg}$ shell nuclei