On the relationship between instability and Lyapunov times for the 3-body problem

In this study we consider the relationship between the survival time and the Lyapunov time for 3-body systems. It is shown that the Sitnikov problem exhibits a two-part power law relationship as demonstrated previously for the general 3-body problem. Using an approximate Poincare map on an appropriate surface of section, we delineate escape regions in a domain of initial conditions and use these regions to analytically obtain a new functional relationship between the Lyapunov time and the survival time for the 3-body problem. The marginal probability distributions of the Lyapunov and survival times are discussed and we show that the probability density function of Lyapunov times for the Sitnikov problem is similar to that for the general 3-body problem.Comment: 9 pages, 19 figures, accepted for publication in MNRA

The role of causal beliefs in political identity and voting

An emerging literature in psychology and political science has identified political identity as an important driver of political decisions. However, less is known about how a person’s political identity is incorporated into their broader self-concept and why it influences some people more than others. We examined the role of political identity in representations of the self-concept as one determinant of people’s political behaviors. We tested the predictions of a recent theoretical account of self-concept representation that, inspired by work on conceptual representation, emphasizes the role of causal beliefs. This account predicts that people who believe that their political identity is causally central (linked to many other features of the self-concept) will be more likely to engage in behaviors consistent with their political identity than those who believe that the same aspect is causally peripheral (linked to fewer other features). Consistent with these predictions, in a study run when political identity was particularly salient—during the 2016 U.S. Presidential election—we found that U.S. voters who believed their political party identity was more causally central (vs those who believe it was causally peripheral) were more likely to vote for their political party’s candidate. Further, in 2 studies, we found that U.K. residents who believed that their English or British national identity was more causally central were more likely to support the U.K. leaving the European Union (Brexit) than those who believed the same identities were more causally peripheral

Representations of the Self-Concept and Identity-Based Choice

We propose a novel approach to identity-based choice that focuses on peoples’ representations of the cause-effect relationships that exist among features of their self-concepts. More specifically, we propose that people who believe that a specific aspect of identity, such as a social category, is causally central (linked to many other features of the self-concept) are more likely to engage in behaviors consistent with that aspect than those who believe that the same aspect is causally peripheral (linked to fewer other features). Across three studies, we provide evidence for our approach to identity-based choice. We demonstrate that among people who belong to the same social category, those who believe that the associated identity is more causally central are more likely to engage in behaviors consistent with the social category

Shadowing unstable orbits of the Sitnikov elliptic 3-body problem

Errors in numerical simulations of gravitating systems can be magnified exponentially over short periods of time. Numerical shadowing provides a way of demonstrating that the dynamics represented by numerical simulations are representative of true dynamics. Using the Sitnikov Problem as an example, it is demonstrated that unstable orbits of the 3-body problem can be shadowed for long periods of time. In addition, it is shown that the stretching of phase space near escape and capture regions is a cause for the failure of the shadowing refinement procedure.Comment: 9 pages, 13 figures, accepted in MNRA

Is the Self-Concept like other Concepts? The Causal Structure of Identity

We investigate the age-old questions of what makes us whowe are and what features of identity, if changed, would makeus a different person. Previous approaches to identity havesuggested that there is a type of feature that is most definingof identity (e.g., autobiographical memories or moralqualities). We propose a new approach to identity thatsuggests that, like concepts in general, more causally centralfeatures are perceived as more defining of the self-concept. Inthree experiments, using both measured and manipulatedcausal centrality, we find that changes to features of identitythat are perceived as more causally central are moredisruptive to both the identity of the self and others

Neglecting Decline: Biased Views of Personal Development Driven By Failure to Recall and Predict Negative Change

A one-year longitudinal study examined people's beliefs about their personal change. Comparisons of predicted, actual, and remembered change revealed that participants simultaneously underestimated the absolute magnitude and overestimated the positivity of change in both prediction and recall. This effect was due to an asymmetry whereby people selectively neglect negative changes

Disruption of the three-body gravitational systems: Lifetime statistics

We investigate statistics of the decay process in the equal-mass three-body problem with randomized initial conditions. Contrary to earlier expectations of similarity with "radioactive decay", the lifetime distributions obtained in our numerical experiments turn out to be heavy-tailed, i.e. the tails are not exponential, but algebraic. The computed power-law index for the differential distribution is within the narrow range, approximately from -1.7 to -1.4, depending on the virial coefficient. Possible applications of our results to studies of the dynamics of triple stars known to be at the edge of disruption are considered.Comment: 13 pages, 2 tables, 3 figure

We Do What We Are: Representation of the Self-Concept and Identity-Based Choice

The current research proposes a novel approach to identity-based choice that focuses on consumers’ representations of the self-concept, as captured by the perceived cause-effect relationships among features of an individual consumer’s self-concept. More specifically, the studies reported here test the proposal that the causal centrality of an identity—the number of other features of a consumer’s self-concept that the consumer believes influenced or were influenced by the identity—underlies identity importance and is a determinant of identity-based consumer behaviors. Across seven studies, using both measured and manipulated causal centrality, the current research provides evidence for the role of causal centrality in identity-based choice. Among consumers who share an identity (belong to the same social category), those who believe that the identity is more causally central perceive the identity as more important and are more likely to engage in behaviors consistent with the norms of the social category

Time matters less when outcomes differ: uni-modal versus cross-modal comparisons in intertemporal choice

Uni-modal intertemporal decisions involve comparing options of the same type (e.g. apples now versus apples later), and cross-modal decisions involve comparing options of different types (e.g. a car now versus a vacation later). As we explain, existing models of intertemporal choice do not allow time preference to depend on whether the comparisons to be made are uni-modal or cross-modal. We test this restriction in an experiment using the delayed-compensation method, a new extension of the standard method of eliciting intertemporal preferences that allows for assessment of time preference for non-monetary and discrete outcomes, as well as for both cross-modal and uni-modal comparisons. Participants were much more averse to delay for uni-modal than cross-modal decisions. We provide two potential explanations for this effect: one drawing on multi-attribute choice, the other drawing on construal level theory