Complex dynamics in equilibrium asset pricing models with boundedly rational,heterogeneous agents

We study a simple model based upon the Lucas framework where heterogeneous agents behave rationally in a fully intertemporal setting but do not know other investors' personal preferences, wealth or investment portfolios. As a consequence, agents initially do not know the equilibrium asset pricing function and must make guesses, which they update via adaptive learning with constant gain. We demonstrate that even in this simple environment the economy can, depending on parameters, exhibit either stable convergence to equilibrium, or chaotic dynamical behavior of asset prices and trading volume without converging to the rational expectations equilibrium of the Lucas model. This contradicts the assertion that the Lucas model is stable in the face of modest deviations from the strong assumptions required to compute the equilibrium. © 2013 Wiley Periodicals, Inc. Complexity 19: 38–55, 2014     

Mechanical properties and thermal conductivity of the twisted graphene nanoribbons

Molecular dynamics method was used to simulate the twists of four GNRs (graphene nanoribbons), two AGNRs (armchair GNRs), and two ZGNRs (zigzag GNRs). Thermal conductivity of the length-fixing GNRs under torsion and at high temperature was calculated. It is found that the ZGNRs have better torsional rigidity than the AGNRs; under the torsional deformation of 34.2°/nm local buckling occurs in the length-fixing GNRs, and under the deformation of 22.8°/nm overall buckling occurs in the ones with free-length. In the range of investigated twist-angle and temperature, the thermal conductivity of the length-fixing GNRs decreases with the increase of torsional deformation and temperature. The wider GNRs have better anti-torsion capability and thermal conductivity.     

Modification of hydrophilic channels in Nafion membranes by DMBA: Mechanism and effects on proton conductivity

Modification of proton conductive channels (PCCs) in Nafion has been achieved with the assistance of 3, 4‐dimethylbenzaldehyde (DMBA). During annealing, ionic clusters develop from small isolated spheres (1.72 nm) to wide continuous channels (5.15 nm), and the crystallinity of Nafion/DMBA membranes is also improved from 17% to 32% as shown by X‐ray diffraction. Molecular dynamic simulation reveals that hydrogen bonding and hydrophobic interaction between DMBA and Nafion work synergistically to achieve better phase separation. The morphology–property relationship shows that, versus various PCCs width, the corresponding proton conductivities vary greatly from 0.079 to 0.139 S/cm at 80 °C. By carefully tuning the width of PCCs, the proton conductivity shows an improvement of 22–34% as compared with pristine Nafion. A significant enhancement on the maximum power density is achieved for the membrane electrode assembly on Nafion/DMBA‐8h (as high as 1018 mW/cm^?2), yielding an enhancement of 39% on pristine Nafion‐8h (730 mW/cm^?2). © 2014 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2014 52, 1107–1117     

Evolving a three-world framework for solving algebraic equations in the light of what a student has met before

In this paper we consider data from a study in which students shift from linear to quadratic equations in ways that do not conform to established theoretical frameworks. In solving linear equations, the students did not exhibit the ‘didactic cut’ of Filloy and Rojano (1989) or the subtleties arising from conceiving an equation as a balance (Vlassis, 2002). Instead they used ‘procedural embodiments’, shifting terms around with added ‘rules’ to obtain the correct answer (Lima & Tall, 2008). Faced with quadratic equations, the students learn to apply the formula with little success. The interpretation of this data requires earlier theories to be seen within a more comprehensive framework that places them in an evolving context. We use the developing framework of three worlds of mathematics (Tall, 2004, Tall, 2013), based fundamentally on human perceptions and actions and their consequences, at each stage taking into account the experiences that students have ‘met-before’ (Lima and Tall, 2008, McGowen and Tall, 2010). These experiences may be supportive in new contexts, encouraging pleasurable generalization, or problematic, causing confusion and even mathematical anxiety. We consider how this framework explains and predicts the observed data, how it evolves from earlier theories, and how it gives insights that have both theoretical and practical consequences.     

Supramolecular Assemblies for Electronic Materials

This work presents a synergy between organic electronics and supramolecular chemistry, in which a host–guest complex is designed to function as an efficacious electronic material. Specifically, the noncovalent recognition of a fullerene, phenyl-C₆₁-butyric acid methyl ester ( PC₆₁BM ), by an alternating perylene diimide ( P )-bithiophene ( B ) conjugated macrocycle ( PBPB ) results in a greater than five-fold enhancement in electron mobility, relative to the macrocycle alone. Characterization and quantification of the binding of fullerenes by host PBPB is provided alongside evidence for intermolecular electronic communication within the host–guest complexes.     

Behavior of metal complexes of polyacrylic acid in solutions

Metal complexes of polyacrylic acid containing Li, Li, and Cu, or Li and Zn have been studied in saline aqueous solutions using molecular hydrodynamics and light scattering methods. Intrinsic viscosities, weight-average molar masses, hydrodynamic radii, and radii of gyration were obtained. It was shown that the macromolecules of polymetalloacrylates containing divalent metals form small and large supramolecular structures, their dimensions, and composition being dependent on the ionic strength of the solution.     

Unravelling the Time Scale of Conformational Plasticity and Allostery in Glycan Recognition by Human Galectin-1

The interaction of human galectin-1 with a variety of oligosaccharides, from di-(N-acetyllactosamine) to tetra-saccharides (blood B type-II antigen) has been scrutinized by using a combined approach of different NMR experiments, molecular dynamics (MD) simulations, and isothermal titration calorimetry. Ligand- and receptor-based NMR experiments assisted by computational methods allowed proposing three-dimensional structures for the different complexes, which explained the lack of enthalpy gain when increasing the chemical complexity of the glycan. Interestingly, and independently of the glycan ligand, the entropy term does not oppose the binding event, a rather unusual feature for protein-sugar interactions. CLEANEX-PM and relaxation dispersion experiments revealed that sugar binding affected residues far from the binding site and described significant changes in the dynamics of the protein. In particular, motions in the microsecond-millisecond timescale in residues at the protein dimer interface were identified in the presence of high affinity ligands. The dynamic process was further explored by extensive MD simulations, which provided additional support for the existence of allostery in glycan recognition by human galectin-1.     

Amorphous polymerization of nitrogen in compressed cupric azide

Metal azides have attracted increasing attention as precursors for synthesizing polymeric nitrogen. In this article, we report the amorphous polymerization of nitrogen by compressing cupric azide. The ab initio molecular dynamics simulations show that crystalline cupric azide transforms into a disordered network composed of singly bonded nitrogen at a hydrostatic pressure of 40 GPa and room temperature. The transformation manifests the formation of a π delocalization along the disordered Cu-N network, thus resulting in a semiconductor–metal transition. The estimated heat of formation of the amorphous polymeric nitrogen system is comparable to conventional high-energy-density materials. The amorphization provides an alternative route to the polymerization of nitrogen under moderate conditions.     

Coexistence and harvesting control policy in a food chain model with mutual defense of prey

A model is proposed to understand the dynamics in a food chain (one predator‐two prey). Unlike many approaches, we consider mutualism (for defense against predators) between the two groups of prey. We investigate the conditions for coexistence and exclusion. Unlike Elettreby's (2009) results, we show that prey can coexist in the absence of predators (as expected since there is no competition between prey). We also show the existence of Hopf bifurcation and limit cycle in the model, and numerically present bifurcation diagrams in terms of mutualism and harvesting. When the harvest is practiced for profit making, we provide the threshold effort value that determines the profitability of the harvest. We show that there is zero profit when the constant effort is applied. Below (resp. above) , there will always be gain (resp. loss). In the case of gain, we provide the optimal effort and optimal steady states that produce maximum profit and ensure coexistence. Recommendations for resource managers As a result of our investigation, we bring the following to the attention of management:

• 1. In the absence of predators, different groups of prey can coexist if they mutually help each other (no competition among them).
• 2. There is a maximal effort to invest in order to gain profit from the harvest. Above , the investment will result in a loss.
• 3. In the case of profit from harvest, policy makers should recommend the optimal effort to be applied and the optimal stock to harvest. This will guarantee maximum profit while ensuring sustainability of all species.