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Liquids are condensed matter in which atoms are strongly correlated in position and momentum. The atomic pair density function (PDF) is used often in describing such correlation. However, elucidation of many properties requires higher degrees of correlation than the pair correlation. For instance, viscosity depends upon the stress correlations in space and time. In this paper, we examine the cross correlation between the stress correlation at the atomic level and the PDF for two-dimensional liquids. We introduce the concept of the stress-resolved pair distribution function (SRPDF) that uses the sign of atomic-level stress as a selection rule to include particles from density correlations. The connection between SRPDFs and stress correlation function is explained through an approximation in which the shear stress is replaced by a pseudospin. We further assess the possibility of interpreting the long-range stress correlation as a consequence of short-range Ising-like pseudospin interactions. [ABSTRACT FROM AUTHOR]

Globalization facilitates our communication with each other, while it magnifies problems such as overharvesting of natural resources and human-induced climate change. Thus people all over the world are involved in a global social dilemma which calls for worldwide cooperation to reduce the risks of these extreme events and disasters. A collective target (threshold) is required to prevent such events. Everyone may lose their wealth once their total individual contributions fail to reach the threshold. To this end, we establish a model of threshold public goods games in a group-structured population and investigate its evolutionary process. We study multilevel public goods games with defectors, local cooperators, and global cooperators and are primarily concerned with how the global cooperative behavior evolves. We find that, compared with the standard public goods games, the strategy of global cooperation accounts for a bigger proportion in the stationary distribution of threshold public goods games. On the other hand, the fixation time of the global cooperation strategy is greatly shortened with increase of the probability of disaster striking. Therefore, global risks induced by the threshold can effectively promote global cooperation in environmental investment and the reduction of greenhouse gas emissions. [ABSTRACT FROM AUTHOR]