scholarly journals Role of weakest links and system-size scaling in multiscale modeling of stochastic plasticity

2017 ◽  
Vol 95 (5) ◽  
Author(s):  
Péter Dusán Ispánovity ◽  
Dániel Tüzes ◽  
Péter Szabó ◽  
Michael Zaiser ◽  
István Groma
Keyword(s):  
Multiscale Modeling ◽  
System Size ◽  
Size Scaling

Phase Transitions, Critical Phenomena, and Finite-Size Scaling

2019 ◽  
pp. 111-176
Author(s):  
Hans-Peter Eckle
Keyword(s):  
Phase Transition ◽  
Phase Transitions ◽  
Critical Phenomena ◽  
Quantum Phase Transitions ◽  
Finite Size ◽  
System Size ◽  
Thermal Fluctuations ◽  
Finite Size Scaling ◽  
Size Scaling

Interacting many-particle systems may undergo phase transitions and exhibit critical phenomena in the limit of infinite system size, while the precursors of these phenomena are studied in the theory of finite-size scaling. After surveying the basic notions of phases, phase diagrams, and phase transitions, this chapter focuses on critical behaviour at a second-order phase transition. The Landau-Ginzburg theory and the concept of scaling prepare readers for an elementary introduction to the concepts of the renormalization group, followed by an introduction into the field of quantum phase transitions where quantum fluctuations take over the role of thermal fluctuations.

scholarly journals Regulation of the normalized rate of driven magnetic reconnection through shocked flux pileup

2021 ◽  
Vol 87 (3) ◽  
Author(s):  
Joseph Olson ◽  
Jan Egedal ◽  
Michael Clark ◽  
Douglass A. Endrizzi ◽  
Samuel Greess ◽  
...  
Keyword(s):  
Magnetic Reconnection ◽  
System Size ◽  
Force Balance ◽  
Absolute Rate ◽  
Reconnection Rate ◽  
Supersonic Plasma ◽  
Reconnection Layer ◽  
Inflow Conditions ◽  
Theoretical Results

Magnetic reconnection is explored on the Terrestrial Reconnection Experiment (TREX) for asymmetric inflow conditions and in a configuration where the absolute rate of reconnection is set by an external drive. Magnetic pileup enhances the upstream magnetic field of the high-density inflow, leading to an increased upstream Alfvén speed and helping to lower the normalized reconnection rate to values expected from theoretical consideration. In addition, a shock interface between the far upstream supersonic plasma inflow and the region of magnetic flux pileup is observed, important to the overall force balance of the system, thereby demonstrating the role of shock formation for configurations including a supersonically driven inflow. Despite the specialized geometry where a strong reconnection drive is applied from only one side of the reconnection layer, previous numerical and theoretical results remain robust and are shown to accurately predict the normalized rate of reconnection for the range of system sizes considered. This experimental rate of reconnection is dependent on system size, reaching values as high as 0.8 at the smallest normalized system size applied.

scholarly journals Noise Response of P53 Oscillation against System Size Scaling

2015 ◽  
Vol 108 (2) ◽  
pp. 150a
Author(s):  
Chong He Yue ◽  
Lock Chew
Keyword(s):  
System Size ◽  
Size Scaling

scholarly journals Strangeness freeze-out: role of system size and missing resonances

2018 ◽  
Vol 171 ◽  
pp. 14002
Author(s):  
Sandeep Chatterjee ◽  
Sabita Das ◽  
Ajay Kumar Dash ◽  
Debadeepti Mishra ◽  
Bedangadas Mohanty ◽  
...  
Keyword(s):  
Size Dependence ◽  
System Size ◽  
Conventional Approach ◽  
Strangeness Production ◽  
Additional Parameter ◽  
Theoretical Approaches ◽  
Missing Resonances ◽  
Freeze Out

The conventional approach to treat strangeness freezeout has been to consider a unified freezeout scheme where strangeness freezes out along with the nonstrange hadrons (1CFO), with or without an additional parameter accounting for out-of-equilibrium strangeness production (γS). Several alternate scenarios have been formulated lately. Here, we will focus on flavor dependent freezeout with early freezeout of strangeness (2CFO) in comparison to 1CFO and its variants with respect to the roles played by the system size and missing resonances predicted by different theoretical approaches but yet to be seen in experiments. In contrast to the performance of 1CFO with/without γS that is insensitive to system size, 2CFO exhibits a clear system size dependence-while for Pb+Pb the χ2/NDF is around 0-2, for smaller system size in p+Pb and p+p, the χ2/NDF> 5 and larger than 1CFO+γS. This clearly shows a system size dependence of the preference for the freezeout scheme, while 2CFO is preferred in Pb+Pb, 1CFO+γS is preferred in p+Pb and p+p. We have further investigated the role of the missing resonances on strangeness freezeout across SPS to LHC beam energies.

scholarly journals On the role of system size in Hall MHD magnetic reconnection

2018 ◽  
Vol 25 (2) ◽  
pp. 022103 ◽  
Author(s):  
C. Bard ◽  
J. C. Dorelli
Keyword(s):  
Magnetic Reconnection ◽  
System Size ◽  
Hall Mhd

Multiscale modeling of brain dynamics depends upon approximations at each scale

1996 ◽  
Vol 19 (2) ◽  
pp. 310-320
Author(s):  
J. J. Wright ◽  
D. T. J. Liley
Keyword(s):  
Multiscale Modeling ◽  
Future Development ◽  
Gamma Band ◽  
Brain Dynamics ◽  
Memory Processes ◽  
Future Developments ◽  
Physiological Information ◽  
The Brain

AbstractWe outline fresh findings that show that our macroscopic electrocorticographic (ECoG) simulations can account for synchronous multiunit pulse oscillations at separate, simultaneously activated cortical sites and the associated gamma-band ECoG activity. We clarify our views on the approximations of dynamic class applicable to neural events at macroscopic and microscopic scales, and the analogies drawn to classes of ANN behaviour. We accept the need to introduce memory processes and detailed anatomical and physiological information into any future developments of our simulations. On the issue of intrinsic cortical stability and the role of extrinsic fibre systems in maintaining stability, we argue that this position is not in extreme contradiction to those of our commentators, and that the mechanisms implicit in our simulations' properties imply rich computational possibilities. We discuss some of the reasons for and against the existence of significant global resonances in the brain and explain why such behaviour appears absent in our simulations. Last, we discuss other phenomena, such as rhythmic driving of the cortex, which have not yet been introduced into our models, and indicate lines for future development of the simulations.

scholarly journals Coordination and Equilibrium Selection in Games: The Role of Local Effects

2021 ◽  
Author(s):  
Tomasz Raducha ◽  
Maxi San Miguel
Keyword(s):  
Replicator Dynamics ◽  
Equilibrium Selection ◽  
System Size ◽  
Critical Value ◽  
Dominant Strategy ◽  
Coordination Games ◽  
Coordination Game ◽  
Local Effects ◽  
Update Rules

Abstract We study the role of local effects and finite size effects in reaching coordination and in equilibrium selection in two-player coordination games. We investigate three update rules – the replicator dynamics (RD), the best response (BR), and the unconditional imitation (UI). For the pure coordination game with two equivalent strategies we find a transition from a disordered state to coordination for a critical value of connectivity. The transition is system-size-independent for the BR and RD update rules. For the IU it is system-size-dependent, but coordination can always be reached below the connectivity of a complete graph. We also consider the general coordination game which covers a range of games, such as the stag hunt. For these games there is a payoff-dominant strategy and a risk-dominant strategy with associated states of equilibrium coordination. We analyse equilibrium selection analytically and numerically. For the RD and BR update rules mean-field predictions agree with simulations and the risk-dominant strategy is evolutionary favoured independently of local effects. When players use the unconditional imitation, however, we observe coordination in the payoff-dominant strategy. Surprisingly, the selection of pay-off dominant equilibrium only occurs below a critical value of the network connectivity and disappears in complete graphs. As we show, it is a combination of local effects and update rule that allows for coordination on the payoff-dominant strategy.

Stretched-exponential relaxation: the role of system size

1998 ◽  
Vol 77 (5) ◽  
pp. 1323-1329 ◽  
Author(s):  
Armin Bunde, Shlomo Havlin, Joseph Klafte
Keyword(s):  
System Size ◽  
Stretched Exponential ◽  
Exponential Relaxation
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