Uniform-in-time continuum limit of the lattice Winfree model and emergent dynamics

<p style='text-indent:20px;'>We study a uniform-in-time continuum limit of the lattice Winfree model(LWM) and its asymptotic dynamics which depends on system functions such as natural frequency function and coupling strength function. The continuum Winfree model(CWM) is an integro-differential equation for the temporal evolution of Winfree phase field. The LWM describes synchronous behavior of weakly coupled Winfree oscillators on a lattice lying in a compact region. For bounded measurable initial phase field, we establish a global well-posedness of classical solutions to the CWM under suitable assumptions on coupling function, and we also show that a classical solution to the CWM can be obtained as a <inline-formula><tex-math id="M1">\begin{document}$ L^1 $\end{document}</tex-math></inline-formula>-limit of a sequence of lattice solutions. Moreover, in the presence of frustration effect, we show that stationary states and bump states can emerge from some admissible class of initial data in a large and intermediate coupling regimes, respectively. We also provide several numerical examples and compare them with analytical results.</p>

Investigating the impact of jury sentencing recommendations using procedural justice theory

Public confidence in the criminal justice system is critical for the system to function effectively. Two studies investigated the impact of jury sentencing recommendations on public confidence using procedural justice theory. The first study (N = 80) manipulated the presence of jury involvement in sentencing (voice present versus voice absent) and the punitiveness of the minimum nonparole period (more punitive versus less punitive) to examine whether giving juries a "voice" - a key element of procedural justice - would increase public confidence in the courts, as well as perceptions of fairness and legitimacy. Contrary to predictions, results revealed that a more punitive sentence led to increased perceptions of legitimacy, which was associated with higher confidence. The second study (N = 60) examined whether manipulating the Judge's agreement with the jury's recommendation - as well as the Judge's reason for disagreement - would elicit the "frustration effect," leading to a decrease in confidence and perceptions of fairness and legitimacy. There was no evidence to suggest that the frustration effect was present. Results of both studies could suggest that jury sentencing recommendations may not effectively increase public confidence and perceptions of fairness and legitimacy in the courts, however alternate explanations are discussed.

Investigating the Impact of Jury Sentencing Recommendations Using Procedural Justice Theory

Public confidence in the criminal justice system is critical for the system to function effectively. Two studies investigated the impact of jury sentencing recommendations on public confidence using procedural justice theory. The first study (N = 80) manipulated the presence of jury involvement in sentencing (voice present versus voice absent) and the punitiveness of the minimum non-parole period (more punitive versus less punitive) to examine whether giving juries a “voice”—a key element of procedural justice—would increase public confidence in the courts, as well as perceptions of fairness and legitimacy. Contrary to predictions, results revealed that a more punitive sentence led to increased perceptions of legitimacy, which was associated with higher confidence. The second study (N = 60) examined whether manipulating the Judge’s agreement with the jury’s recommendation—as well as the Judge’s reason for disagreement—would elicit the “frustration effect,” leading to a decrease in confidence and perceptions of fairness and legitimacy. There was no evidence to suggest that the frustration effect was present. Results of both studies could suggest that jury sentencing recommendations may not effectively increase public confidence and perceptions of fairness and legitimacy in the courts, however alternate explanations are discussed.

LONG-RANGE ELECTRON HOPPING AND FERROMAGNETISM IN CLUSTERS

In the present paper, we investigate the frustration effect caused by the long-range electron hopping on ferromagnetism in atomic or molecular clusters. First, for an idealized Hubbard model with constant electron hopping amplitude, we prove rigorously that interplay between such frustration effect and the on-site Coulomb interaction produces the saturated ferromagnetism when the cluster is slightly doped with electron. Then, by exact diagonalization calculation, we study some more realistic clusters and show that the ferromagnetic ground state is still stable as long as the Coulomb repulsion interaction between electrons is sufficiently strong.