Opinion strength influences the spatial dynamics of opinion formation

Opinions are rarely binary; they can be held with different degrees of conviction, and this expanded attitude spectrum can affect the influence one opinion has on others. Our goal is to understand how different aspects of influence lead to recognizable spatio-temporal patterns of opinions and their strengths. To do this, we introduce a stochastic spatial agent-based model of opinion dynamics that includes a spectrum of opinion strengths and various possible rules for how the opinion strength of one individual affects the influence that this individual has on others. Through simulations, we find that even a small amount of amplification of opinion strength through interaction with like-minded neighbors can tip the scales in favor of polarization and deadlock

Piloted simulator study of allowable time delays in large-airplane response

A piloted simulation was performed to determine the permissible time delay and phase shift in the flight control system of a specific large transport-type airplane. The study was conducted with a six degree of freedom ground-based simulator and a math model similar to an advanced wide-body jet transport. Time delays in discrete and lagged form were incorporated into the longitudinal, lateral, and directional control systems of the airplane. Three experienced pilots flew simulated approaches and landings with random localizer and glide slope offsets during instrument tracking as their principal evaluation task. Results of the present study suggest a level 1 (satisfactory) handling qualities limit for the effective time delay of 0.15 sec in both the pitch and roll axes, as opposed to a 0.10-sec limit of the present specification (MIL-F-8785C) for both axes. Also, the present results suggest a level 2 (acceptable but unsatisfactory) handling qualities limit for an effective time delay of 0.82 sec and 0.57 sec for the pitch and roll axes, respectively, as opposed to 0.20 sec of the present specifications for both axes. In the area of phase shift between cockpit input and control surface deflection,the results of this study, flown in turbulent air, suggest less severe phase shift limitations for the approach and landing task-approximately 50 deg. in pitch and 40 deg. in roll - as opposed to 15 deg. of the present specifications for both axes

Transient electrophoretic current in a nonpolar solvent

The transient electric current of surfactants dissolved in a nonpolar solvent is investigated both experimentally and theoretically in the parallel-plate geometry. Due to a low concentration of free charges the cell can be completely polarized by an external voltage of several volts. In this state, all the charged micelles are compacted against the electrodes. After the voltage is set to zero the reverse current features a sharp discharge spike and a broad peak. This shape and its variation with the compacting voltage are reproduced in a one-dimensional drift-diffusion model. The model reveals the broad peak is formed by a competition between an increasing number of charges drifting back to the middle of the cell and a decreasing electric field that drives the motion. After complete polarization is achieved, the shape of the peak stops evolving with further increase of the compacting voltage. The spike-peak separation time grows logarithmically with the charge content in the bulk. The time peak is a useful measure of the micelle mobility. Time integration of the peak yields the total charge in the system. By measuring its variation with temperature, the activation energy of bulk charge generation has been found to be 0.126 eV.Comment: 7 pages, 5 figure

Heisenberg antiferromagnet with anisotropic exchange on the Kagome lattice: Description of the magnetic properties of volborthite

We study the properties of the Heisenberg antiferromagnet with spatially anisotropic nearest-neighbour exchange couplings on the kagome net, i.e. with coupling J in one lattice direction and couplings J' along the other two directions. For J/J' > 1, this model is believed to describe the magnetic properties of the mineral volborthite. In the classical limit, it exhibits two kinds of ground states: a ferrimagnetic state for J/J' < 1/2 and a large manifold of canted spin states for J/J' > 1/2. To include quantum effects self-consistently, we investigate the Sp(N) symmetric generalisation of the original SU(2) symmetric model in the large-N limit. In addition to the dependence on the anisotropy, the Sp(N) symmetric model depends on a parameter kappa that measures the importance of quantum effects. Our numerical calculations reveal that in the kappa-J/J' plane, the system shows a rich phase diagram containing a ferrimagnetic phase, an incommensurate phase, and a decoupled chain phase, the latter two with short- and long-range order. We corroborate these results by showing that the boundaries between the various phases and several other features of the Sp(N) phase diagram can be determined by analytical calculations. Finally, the application of a block-spin perturbation expansion to the trimerised version of the original spin-1/2 model leads us to suggest that in the limit of strong anisotropy, J/J' >> 1, the ground state of the original model is a collinearly ordered antiferromagnet, which is separated from the incommensurate state by a quantum phase transition.Comment: 21 pages, 22 figures. Final version, PRB in pres

Spatial opinion dynamics and the effects of two types of mixing

Spatially situated opinions that can be held with different degrees of conviction lead to spatiotemporal patterns such as clustering (homophily), polarization, and deadlock. Our goal is to understand how sensitive these patterns are to changes in the local nature of interactions. We introduce two different mixing mechanisms, spatial relocation and nonlocal interaction (“telephoning”), to an earlier fully spatial model (no mixing). Interestingly, the mechanisms that create deadlock in the fully spatial model have the opposite effect when there is a sufficient amount of mixing. With telephoning, not only is polarization and deadlock broken up, but consensus is hastened. The effects of mixing by relocation are even more pronounced. Further insight into these dynamics is obtained for selected parameter regimes via comparison to the mean-field differential equations

Ordering the braid groups

We give an explicit geometric argument that Artin's braid group $B_n$ is right-orderable. The construction is elementary, natural, and leads to a new, effectively computable, canonical form for braids which we call left-consistent canonical form. The left-consistent form of a braid which is positive (respectively negative) in our order has consistently positive (respectively negative) exponent in the smallest braid generator which occurs. It follows that our ordering is identical to that of Dehornoy, constructed by very different means, and we recover Dehornoy's main theorem that any braid can be put into such a form using either positive or negative exponent in the smallest generator but not both. Our definition of order is strongly connected with Mosher's normal form and this leads to an algorithm to decide whether a given braid is positive, trivial, or negative which is quadratic in the length of the braid word.Comment: 24 pages, 10 figure

Plant responses to sublethal concentrations of 2,4-D

Typescript (photocopy) Thesis (M.S.)--Iowa State University, 1967. Includes bibliography