45 research outputs found
Beta-rhythm oscillations and synchronization transition in network models of Izhikevich neurons: effect of topology and synaptic type
Despite their significant functional roles, beta-band oscillations are least
understood. Synchronization in neuronal networks have attracted much attention
in recent years with the main focus on transition type. Whether one obtains
explosive transition or a continuous transition is an important feature of the
neuronal network which can depend on network structure as well as synaptic
types. In this study we consider the effect of synaptic interaction (electrical
and chemical) as well as structural connectivity on synchronization transition
in network models of Izhikevich neurons which spike regularly with beta
rhythms. We find a wide range of behavior including continuous transition,
explosive transition, as well as lack of global order. The stronger electrical
synapses are more conducive to synchronization and can even lead to explosive
synchronization. The key network element which determines the order of
transition is found to be the clustering coefficient and not the small world
effect, or the existence of hubs in a network. These results are in contrast to
previous results which use phase oscillator models such as the Kuramoto model.
Furthermore, we show that the patterns of synchronization changes when one goes
to the gamma band. We attribute such a change to the change in the refractory
period of Izhikevich neurons which changes significantly with frequency.Comment: 7 figures, 1 tabl
Critical behaviour and microscopic structure of charged AdS black holes via an alternative phase space
It has been argued that charged Ads black holes have similar thermodynamic
behavior as the Van der Waals fluid system, provided one treats the
cosmological constant as a thermodynamic variable in an extended phase space.
In this paper, we disclose the deep connection between charged AdS black holes
and Van der Waals fluid system without extending the phase space. We keep the
cosmological constant as a fixed parameter and instead, treat the square of the
charge of black hole as a thermodynamic variable. Therefore, we write the
equation of state as where (conjugate of )
is the inverse of the specific volume, . This allows us to complete
the analogy of charged AdS black holes with Van der Waals fluid system and
derive the phase transition as well as critical exponents of the system. We
identify a thermodynamic instability in this new picture with real analogy to
Van der Waals fluid with physically relevant Maxwell construction. We therefore
study the critical behavior of isotherms in diagram and deduce all
the critical exponents of the system and determine that the system exhibits a
small-large black hole phase transition at the critical point . This alternative view is important as one can imagine such a change
for a given single black hole i. e. acquiring charge which induces the phase
transition. Finally, we disclose the microscopic properties of charged AdS
black holes by using thermodynamic geometry. Interestingly, we find that scalar
curvature has a gap between small and large black holes, and this gap becomes
exceedingly large as one moves away from the critical point along the
transition line. Therefore, we are able to attribute the sudden enlargement of
the black hole to the strong repulsive nature of the internal constituents at
the phase transition.Comment: 7 pages, 6 figures. New title and a new figure in the second versio