scholarly journals Mean-field approximations for short-range four-body interactions at ν=35

2019 ◽  
Vol 99 (23) ◽  
Author(s):  
Bartosz Kuśmierz ◽  
Arkadiusz Wójs ◽  
G. J. Sreejith
Keyword(s):  
Short Range ◽  
Mean Field ◽  
Mean Field Approximations

scholarly journals Population dynamics with spatial structure and an Allee effect

2020 ◽  
Author(s):  
Anudeep Surendran ◽  
Michael Plank ◽  
Matthew Simpson
Keyword(s):  
Population Dynamics ◽  
Spatial Structure ◽  
Short Range ◽  
Allee Effect ◽  
Mean Field ◽  
Mean Field Approximation ◽  
Continuum Approximation ◽  
Spatial Moment ◽  
Mean Field Models ◽  
The Mean

AbstractAllee effects describe populations in which long-term survival is only possible if the population density is above some threshold level. A simple mathematical model of an Allee effect is one where initial densities below the threshold lead to population extinction, whereas initial densities above the threshold eventually asymptote to some positive carrying capacity density. Mean field models of population dynamics neglect spatial structure that can arise through short-range interactions, such as short-range competition and dispersal. The influence of such non mean-field effects has not been studied in the presence of an Allee effect. To address this we develop an individual-based model (IBM) that incorporates both short-range interactions and an Allee effect. To explore the role of spatial structure we derive a mathematically tractable continuum approximation of the IBM in terms of the dynamics of spatial moments. In the limit of long-range interactions where the mean-field approximation holds, our modelling framework accurately recovers the mean-field Allee threshold. We show that the Allee threshold is sensitive to spatial structure that mean-field models neglect. For example, we show that there are cases where the mean-field model predicts extinction but the population actually survives and vice versa. Through simulations we show that our new spatial moment dynamics model accurately captures the modified Allee threshold in the presence of spatial structure.

scholarly journals Reflections on the origin of the EMC effect

2018 ◽  
Vol 27 (12) ◽  
pp. 1840001 ◽  
Author(s):  
Anthony W. Thomas
Keyword(s):  
Short Range ◽  
Mean Field ◽  
Atomic Nuclei ◽  
Lorentz Scalar ◽  
Valence Structure ◽  
Mean Fields ◽  
European Muon Collaboration ◽  
The Mean ◽  
Emc Effect ◽  
Short Range Correlations

In the 35 years since the European Muon Collaboration announced the astonishing result that the valence structure of a nucleus was very different from that of a free nucleon, many explanations have been suggested. The first of the two most promising explanations is based upon the different effects of the strong Lorentz scalar and vector mean fields known to exist in a nucleus on the internal structure of the nucleon-like clusters which occupy shell model states. The second links the effect to the modification of the structure of nucleons involved in short-range correlations, which are far off their mass shell. We explore some of the methods which have been proposed to give complementary information on this puzzle, especially the spin-dependent EMC effect and the isovector EMC effect, both proposed by Cloët, Bentz and Thomas. It is shown that the predictions for the spin-dependent EMC effect, in particular, differ substantially within the mean-field and short-range correlation approaches. Hence, the measurement of the spin-dependent EMC effect at Jefferson Lab should give us a deeper understanding of the origin of the EMC effect and, indeed, of the structure of atomic nuclei.

EXTENSIONS OF MEAN-FIELD APPROXIMATIONS

1995 ◽  
pp. 17-44
Author(s):  
M. Suzuki ◽  
X. Hu ◽  
N. Hatano ◽  
M. Katori ◽  
K. Minami ◽  
...  
Keyword(s):  
Mean Field ◽  
Mean Field Approximations
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