The pseudo-Jahn—Teller effect: a CASSCF diagnostic

A simple test for the pseudo-Jahn-Teller effect is proposed, based on the behaviour of a CASSCF frequency calculation when symmetry is restricted. The test suggests that the pseudo-Jahn-Teller effect operates at the D_2h transition structure of S₀ pentalene and the D_8h transition structure of S₀ cyclooctatetraene. The D_4h transition structure of S₀ cyclooctatetraene is not subject to a pseudo-Jahn-Teller distortion according to this test. Our interpretation of the pseudo-Jahn-Teller effect differs from the conventional one based on a single-transition (CIS-like) approximation.     

ANALYSIS OF THE MULTIPLE-SOLUTION RESPONSE OF A FLEXIBLE ROTOR SUPPORTED ON NON-LINEAR SQUEEZE FILM DAMPERS

The multiple-solution response of rotors supported on squeeze film dampers is a typical non-linear phenomenon. The behaviour of the multiple-solution response in a flexible rotor supported on two identical squeeze film dampers with centralizing springs is studied by three methods: synchronous circular centred-orbit motion solution, numerical integration method and slow acceleration method using the assumption of a short bearing and cavitated oil film; the differences of computational results obtained by the three different methods are compared in this paper. It is shown that there are three basic forms for the multiple-solution response in the flexible rotor system supported on the squeeze film dampers, which are the resonant, isolated bifurcation and swallowtail bifurcation multiple solutions. In the multiple-solution speed regions, the rotor motion may be subsynchronous, super-subsynchronous, almost-periodic and even chaotic, besides synchronous circular centred, even if the gravity effect is not considered. The assumption of synchronous circular centred-orbit motion for the journal and rotor around the static deflection line can be used only in some special cases; the steady state numerical integration method is very useful, but time consuming. Using the slow acceleration method, not only can the multiple-solution speed regions be detected, but also the non-synchronous response regions.     

The Role of Metanetworks in Network Evolution

The question of what structures of relations between actors emerge in the evolution of social networks is of fundamental sociological interest. The present research proposes that processes of network evolution can be usefully conceptualized in terms of a network of networks, or “metanetwork,” wherein networks that are one link manipulation away from one another are connected. Moreover, the geography of metanetworks has real effects on the course of network evolution. Specifically, both equilibrium and non-equilibrium networks located in more desirable regions of the metanetwork are found to be more probable. These effects of metanetwork geography are illustrated by two dynamic network models: one in which actors pursue access to unique information through “structural holes,” and the other in which actors pursue access to valid information by minimizing path length. Finally, I discuss future directions for modeling network dynamics in terms of metanetworks.     

Testing Ten Theories

Using the most comprehensive data set now available, this investigation tests the precision of all exchange theories that now contend. Beyond precision, the investigation focuses on broad issues of effectiveness including consistency, parsimony, and whether the theories can be applied to structures larger than normally studied in the lab. Seeking greater parsimony, this investigation introduces a new model by combining parts of two contending theories. We find that all ten theories have scientific merit for all can predict with some effectiveness for the exchange structures experimentally investigated. Nevertheless, the ten vary in precision. Elementary Theory is the most precise. The new Expected-value Resistance model ranks second in precision and is the simplest. Both apply to large networks as well as the best of the other theories.     

A Wealth and Status-Based Model of Residential Segregation

We extend the classic “Schelling model” (1971 Schelling , T. C. (1971). Dynamic models of segregation. Journal of Mathematical Sociology , 1, 143–186.[Taylor &; Francis Online], [Web of Science ®] , [Google Scholar] 1978 Schelling , T. C. ( 1978 ). Micromotives and Macrobehavior , New York and London : W.W. Norton and Company . [Google Scholar]) to incorporate the wealth and status of agents and the desirability and affordability of residences. We analyze the effects of 1) the degree of the status-wealth correlation, and 2) the extent to which the wealth of residents shapes the affordability of residences, on levels of status and wealth segregation. Both factors generally exert a positive effect on both forms of segregation and interact to produce higher levels of segregation. The greater the correlation between status and wealth, the more the agents tend to segregate, either due to choice (for the wealthy and high status) or exclusion (for the poor and low status). We also find that housing price endogeneity is a precondition for status segregation.