Four-dimensional topological lattices through connectivity

Thanks to recent advances, the 4D quantum Hall (QH) effect is becoming experimentally accessible in various engineered set-ups. In this paper, we propose a new type of 4D topological system that, unlike other 2D and 4D QH models, does not require complicated (artificial) gauge fields and/or time-reversal symmetry breaking. Instead, we show that there are 4D QH systems that can be engineered for spinless particles by designing the lattice connectivity with real-valued hopping amplitudes, and we explain how this physics can be intuitively understood in analogy with the 2D Haldane model. We illustrate our discussion with a specific 4D lattice proposal, inspired by the widely-studied 2D honeycomb and brickwall lattice geometries. This also provides a minimal model for a topological system in Class AI, which supports nontrivial topological band invariants only in four spatial dimensions or higher

The evolution of leader-follower reciprocity: The theory of service-for-prestige

Copyright © 2014 Price and Van Vugt. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) or licensor are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.This article has been made available through the Brunel Open Access Publishing Fund.We describe the service-for-prestige theory of leadership, which proposes that voluntary leader–follower relations evolved in humans via a process of reciprocal exchange that generated adaptive benefits for both leaders and followers. We propose that although leader–follower relations first emerged in the human lineage to solve problems related to information sharing and social coordination, they ultimately evolved into exchange relationships whereby followers could compensate leaders for services which would otherwise have been prohibitively costly for leaders to provide. In this exchange, leaders incur costs to provide followers with public goods, and in return, followers incur costs to provide leaders with prestige (and associated fitness benefits). Because whole groups of followers tend to gain from leader-provided public goods, and because prestige is costly for followers to produce, the provisioning of prestige to leaders requires solutions to the “free rider” problem of disrespectful followers (who benefit from leader services without sharing the costs of producing prestige). Thus service-for-prestige makes the unique prediction that disrespectful followers of beneficial leaders will be targeted by other followers for punitive sentiment and/or social exclusion. Leader–follower relations should be more reciprocal and mutually beneficial when leaders and followers have more equal social bargaining power. However, as leaders gain more relative power, and their high status becomes less dependent on their willingness to pay the costs of benefitting followers, service-for-prestige predicts that leader–follower relations will become based more on leaders’ ability to dominate and exploit rather than benefit followers. We review evidential support for a set of predictions made by service-for-prestige, and discuss how service-for-prestige relates to social neuroscience research on leadership

Dipotassium [N,N '-(propane-1,3-diyl)dioxamato-kappa O-4,N,N ',O ']copper(II) trihydrate: redetermination at 100 K

Redetermination of the structure of the title compound, K-2[Cu(C7H6N2O6)]center dot 3H(2)O,at 100 K reveals conformational disorder in the almost planar copper-containing molecular dianions and clarifies the complex hydrogen-bonded network involving the water molecules. The asymmetric unit contains two independent formula units. In one of the [Cu(C7H6N2O6)](2-) dianions, the propyl chain is disordered over two orientiations, with site-occupancy factors of 0.852 (5) and 0.148 (5)

Copper(II) complexes with a flexible oxamato ligand

We report on a convenient synthesis of the ligand precursor, diethylethylene-1,2-bis(oxamate), (Et2H2oeo, 1), and show how a partial and preferential hydrolysis of the ester group can give rise to the dianionic ligand, (H2oeo)2−. Reaction of this ligand with Cu(II) affords the neutral dimeric species, [Cu2(H2oeo)2], which has a low aqueous solubility. We describe the crystal structure of the hydrate Cu2(H2oeo)2(H2O)4 (2) and report magnetic studies that show a weak exchange interaction in the solid. Under more basic conditions and in the presence of Cu(II) ions, we are able to avoid amide cleavage and yet deprotonate the amide group, resulting in the formation of the highly soluble [Cu(Hoeo)2]4− complex anion. The structure of (NBu4)4[Cu(Hoeo)2](H2O)4 (3) is described and compared with the recently reported anhydrous phase

Ballistic trajectory: parabola, ellipse, or what?

Mechanics texts tell us that a particle in a bound orbit under gravitational central force moves on an ellipse, while introductory physics texts approximate the earth as flat, and tell us that the particle moves in a parabola. The uniform-gravity, flat-earth parabola is clearly meant to be an approximation to a small segment of the true central-force/ellipse orbit. To look more deeply into this connection we convert earth-centered polar coordinates to ``flat-earth coordinates'' by treating radial lines as vertical, and by treating lines of constant radial distance as horizontal. With the exact trajectory and dynamics in this system, we consider such questions as whether gravity is purely vertical in this picture, and whether the central force nature of gravity is important only when the height or range of a ballistic trajectory is comparable to the earth radius. Somewhat surprisingly, the answers to both questions is ``no,'' and therein lie some interesting lessons.Comment: 7 pages, 3 figure