Conformity and Dissonance in Generalized Voter Models

We generalize the voter model to include social forces that produce conformity among voters and avoidance of cognitive dissonance of opinions within a voter. The time for both conformity and consistency (which we call the exit time) is, in general, much longer than for either process alone. We show that our generalized model can be applied quite widely: it is a form of Wright’s island model of population genetics, and is related to problems in the physical sciences. We give scaling arguments, numerical simulations, and analytic estimates for the exit time for a range of relative strengths in the tendency to conform and to avoid dissonance.     

A Generalized Voter Model on Complex Networks

We study a generalization of the voter model on complex networks, focusing on the scaling of mean exit time. Previous work has defined the voter model in terms of an initially chosen node and a randomly chosen neighbor, which makes it difficult to disentangle the effects of the stochastic process itself relative to the network structure. We introduce a process with two steps, one that selects a pair of interacting nodes and one that determines the direction of interaction as a function of the degrees of the two nodes and a parameter α which sets the likelihood of the higher degree node giving its state to the other node. Traditional voter model behaviors can be recovered within the model, as well as the invasion process. We find that on a complete bipartite network, the voter model is the fastest process. On a random network with power law degree distribution, we observe two regimes. For modest values of α, exit time is dominated by diffusive drift of the system state, but as the high-degree nodes become more influential, the exit time becomes dominated by frustration effects dependent on the exact topology of the network.     

Competing species dynamics: Qualitative advantage versus geography

A simple cellular automata model for a two-group war over the same “territory” is presented. It is shown that a qualitative advantage is not enough for a minority to win. A spatial organization as well a definite degree of aggressiveness are instrumental to overcome a less fitted majority. The model applies to a large spectrum of competing groups: smoker-non smoker war, epidemic spreading, opinion formation, competition for industrial standards and species evolution. In the last case, it provides a new explanation for punctuated equilibria. Received: 21 April 1998 / Revised and Accepted: 22 April 1998     

Decelerating microdynamics can accelerate macrodynamics in the voter model

For the voter model, we study the effect of a memory-dependent transition rate. We assume that the transition of a spin into the opposite state decreases with the time it has been in its current state. Counterintuitively, we find that the time to reach a macroscopically ordered state can be accelerated by slowing down the microscopic dynamics in this way. This holds for different network topologies, including fully connected ones. We find that the ordering dynamics is governed by two competing processes which either stabilize the majority or the minority state. If the first one dominates, it accelerates the ordering of the system. The conclusions of this Letter are not restricted to the voter model, but remain valid to many other spin systems as well.     

The Sound of Silence: Minorities,Abstention and Democracy

Despite the existence of an extensive literature, no definitive conclusion seems to emerge on the extent to which minorities are guaranteed by democratic rules in political systems. This paper contributes to this debate by proposing a modified Heigselmann and Krauss two-dimensional model of preferences in order to capture the role of abstention on minority representativeness. Regardless of the typology of abstention, simulation results show that voter abstention always benefits minorities.     

Heterogenous mean-field analysis of a generalized voter-like model on networks

We propose a generalized framework for the study of voter models in complex networks at the heterogeneous mean-field (HMF) level that (i) yields a unified picture for existing copy/invasion processes and (ii) allows for the introduction of further heterogeneity through degree-selectivity rules. In the context of the HMF approximation, our model is capable of providing straightforward estimates for central quantities such as the exit probability and the consensus/fixation time, based on the statistical properties of the complex network alone. The HMF approach has the advantage of being readily applicable also in those cases in which exact solutions are difficult to work out. Finally, the unified formalism allows one to understand previously proposed voter-like processes as simple limits of the generalized model.     

Anticonformity or Independence?—Insights from Statistical Physics

The aim of this paper is to examine how different types of social influence, introduced on the microscopic (individual) level, manifest on the macroscopic level, i.e. in the society. The inspiration for this task came mainly from two sources—social psychology that recognize two different types of nonconformity (anticonformity and independence) and the observation related to the agent-based modeling that was verbalized in 2002 by Macy and Willer that there was a little effort to provide analysis of how results differ depending on the model designs. To achieve the goal, we propose a generalized model of opinion dynamics, that as a special cases reduces to the linear voter model, Sznajd model, q-voter model and the majority rule. We use the model to examine the differences, that appear at the macroscopic level, under the influence of two types of nonconformity, introduced on the microscopic level. We answer the question if the observed differences are universal or model dependent.     

Local probing of the surface chemical bond using X-ray emission spectroscopy

2 and CO on Ni(100), benzene on Ni(100) and Cu(110), and glycine adsorbed on Cu(110). New types of molecular states are observed which are directly related to the surface chemical bond. The long-accepted Blyholder model which is based on a frontier orbital concept cannot explain our results for N₂ and CO chemisorption. We find it necessary to offer a new picture where changes in the whole molecular orbital framework have to be considered. We show that both π and σ type interactions are important in describing the bonding in benzene to metal surfaces. The future prospect is illustrated by the adsorption of the simplest amino acid, glycine, on Cu(110). The adsorbate has four different atomic centers where X-ray emission spectra are obtained, providing a unique view of the local electronic structure. Accepted: 6 March 1997     

Phase-field study of free growth in a channel: from thermal to chemical solidification

The thermal and the chemical phase-field models for free growth in a two-dimensional channel are both studied in their one-sided version for which diffusion only occurs in the liquid. We compare the steady state fingers obtained in our phase-field simulations with the results of boundary integral techniques available in the literature. The excellent agreement found between both methods provides a valuable benchmark of the one-sided thin-interface phase model which makes use of an antitrapping current. Coexistence of several steady states predicted by the Green’s function calculations is also recovered. The dynamical stability of two competing modes (symmetric and asymmetric finger) is studied and the extension of their respective basins of attraction is evaluated. General implications of our results for a large class of isotropic systems are discussed.     

The minority’s success under majority rule

In this paper, we focus on the effect of a network’s structure on the process of opinion formation. Emphasis is placed on the minority’s opinion evolution in a community structured network, where the majority rule is applied to govern the evolution. A model is developed for theoretical analysis using the mean field method. In this model, the connections are dense in the community, but sparse outside. A bifurcation diagram can thus be constructed, which is also verified through experimental study. The phase transition in the evolution is also investigated. In addition, a further investigation shows that a larger group size would bring more advantage to the minority.     

A Model for Coagulation with Mating

We consider in this work a model for aggregation, where the coalescing particles initially have a certain number of potential links (called arms) which are used to perform coagulations. There are two types of arms, male and female, and two particles may coagulate only if one has an available male arm, and the other has an available female arm. After a coagulation, the used arms are no longer available. We are interested in the concentrations of the different types of particles, which are governed by a modification of Smoluchowski’s coagulation equation—that is, an infinite system of nonlinear differential equations. Using generating functions and solving a nonlinear PDE, we show that, up to some critical time, there is a unique solution to this equation. The Lagrange Inversion Formula allows in some cases to obtain explicit solutions, and to relate our model to two recent models for limited aggregation. We also show that, whenever the critical time is infinite, the concentrations converge to a state where all arms have disappeared, and the distribution of the masses is related to the law of the size of some two-type Galton-Watson tree. Finally, we consider a microscopic model for coagulation: we construct a sequence of Marcus-Lushnikov processes, and show that it converges, before the critical time, to the solution of our modified Smoluchowski’s equation.     

Nonlinear voter models: the transition from invasion to coexistence

In nonlinear voter models the transitions between two states depend in a nonlinear manner on the frequencies of these states in the neighborhood. We investigate the role of these nonlinearities on the global outcome of the dynamics for a homogeneous network where each node is connected to m = 4 neighbors. The paper unfolds in two directions. We first develop a general stochastic framework for frequency dependent processes from which we derive the macroscopic dynamics for key variables, such as global frequencies and correlations. Explicit expressions for both the mean-field limit and the pair approximation are obtained. We then apply these equations to determine a phase diagram in the parameter space that distinguishes between different dynamic regimes. The pair approximation allows us to identify three regimes for nonlinear voter models: (i) complete invasion; (ii) random coexistence; and – most interestingly – (iii) correlated coexistence. These findings are contrasted with predictions from the mean-field phase diagram and are confirmed by extensive computer simulations of the microscopic dynamics.     

Statistics of coherently detected backscatter and range performance of coherent OTDRs

We derive the statistics of a coherently detected backscatter waveform taking into account the effects of polarization. For the first time these statistics are related to measurable parameters. We show that for long-range OTDRs the effects of polarization are statistically small.In relation to the demodulation process we used our statistical model to show that for long-range operation and with heterodyne detection all types of demodulation provide similar performance. With homodyne detection half-wave demodulation results in a 7 dB lower signal-to-noise ratio than the other types of demodulation which have similar performance. There is the usual 3 dB advantage of homodyne over heterodyne detection. Our results indicate that with the same launched powers, the signal obtained from a coherent OTDR can have up to a 37 dB better signal-to-noise ratio than one obtained from an incoherent pulse OTDR. This results in a 9 dB range advantage.We verify previously tabulated results which we found apply only for short-range operation. We use our model to predict the limits of long-range performance and to predict the effect of speckle on averaging. Finally, we explain the breakpoint behaviour that can be seen in results already reported and which is characteristic of linear full- or half-wave envelope demodulation.     

Electronic structure of half-metallic ferromagnet Co<Subscript>2</Subscript>MnSi at high-pressure

In this study, first principles calculation results of the half-metallic ferromagnetic Heusler compound Co₂MnSi are presented. All calculations are based on the spin-polarized generalized gradient approximation (σ-GGA) of the density functional theory and ultrasoft pseudopotentials with plane wave basis. Electronic structure of related compound in cubic L2₁ structure is investigated up to 95 GPa uniform hydrostatic pressure. The half-metal to metal transition was observed around ~70 GPa together with downward shift of the conduction band minimum (CBM) and a linear increase of direct band gap of minority spins at Γ-point with increasing pressure. The electronic density of states of minority spins at Fermi level, which are mainly due to the cobalt atoms, become remarkable with increasing pressure resulting a sharp decrease in spin polarization ratio. It can be stated that the pressure affects minority spin states rather than that of majority spins and lead to a slight reconstruction of minority spin states which lie below the Fermi level. In particular, energy band gap of minority spin states in equilibrium structure is obviously not destroyed, but the Fermi level is shifted outside the gap.     

磁绝缘传输线振荡器中的次级电子倍增现象

根据磁绝缘传输线振荡器(MILO)的结构特点，建立了一个单边次级电子倍增(multipactor)模型，通过对敏感曲线、相位聚焦的计算，分析了MILO中发生multipactor的物理图象.结果表明：从聚焦区域大小看，单边发生multipactor 比双边要严重.在MILO中发生的multipactor都属于单边模式，并且有出现电子掠入射金属表面的大量机会，因此它发生multipactor比O型器件严重. 关键词： 磁绝缘传输线振荡器 次级电子倍增效应 脉冲缩短     

Search for molecular bands in 13C

In a systematic search through experimental results for transfer reactions, inelastic excitations and other data for ¹³C we identify states which have no simple structure related to the low-lying states of ¹²C. We propose that these states have strong α-clustering and that they are related to chain states expected in ^13-14C. The properties of these states are discussed on the basis of a molecular orbital model. Received: 12 December 2001 / Accepted: 3 April 2002     

Phase Transitions for the Growth Rate of Linear Stochastic Evolutions

We consider a discrete-time stochastic growth model on d-dimensional lattice. The growth model describes various interesting examples such as oriented site/bond percolation, directed polymers in random environment, time discretizations of binary contact path process and the voter model. We study the phase transition for the growth rate of the “total number of particles” in this framework. The main results are roughly as follows: If d≥3 and the system is “not too random”, then, with positive probability, the growth rate of the total number of particles is of the same order as its expectation. If on the other hand, d=1,2, or the system is “random enough”, then the growth rate is slower than its expectation. We also discuss the above phase transition for the dual processes and its connection to the structure of invariant measures for the model with proper normalization. Supported in part by JSPS Grant-in-Aid for Scientific Research, Kiban (C) 17540112.     

One-Sided Continuity Properties for the Schonmann Projection

We consider the plus-phase of the two-dimensional Ising model below the critical temperature. In 1989 Schonmann proved that the projection of this measure onto a one-dimensional line is not a Gibbs measure. After many years of continued research which have revealed further properties of this measure, the question whether or not it is a Gibbs measure in an almost sure sense remains open. In this paper we study the same measure by interpreting it as a temporal process. One of our main results is that the Schonmann projection is almost surely a regular g-measure. That is, it does possess the corresponding one-sided notion of almost Gibbsianness. We further deduce strong one-sided mixing properties which are of independent interest. Our proofs make use of classical coupling techniques and some monotonicity properties which are known to hold for one-sided, but not two-sided conditioning for FKG measures.     

Discrete photodetection of quantum jumps on the V configuration of atomic levels

A theory of the discrete photodetection of quantum jumps on the V configuration of atomic levels has been developed. A three-level source atom is placed in a cavity excited by a resonance fluorescence field. The cavity is tuned to exact resonance with an atomic transition. The cavity mode state is tested by a flux of unexcited (at the entrance) probe atoms passing through the cavity. The energy states of the outgoing probe atoms are detected by ionization chambers, which are assumed ideal. This a posteriori statistical information is indirectly related to the numerical characteristics of a measured quantum system consisting of the source atom and cavity mode. The “tuning” conditions for a discrete photodetector, i.e., the rules for choosing the parameters and durations of the interactions of the cavity mode with the probe and source atoms, intensities of the pump and probe fields that are necessary for observing quantum jumps from the “bright” state to the “dark” one and vice versa, have been determined. A two-state model that describes the dynamics of a quantum jump has been analyzed. The formulas have been obtained for the observable characteristics of quantum jumps: the mean residence time of the quantum system in quasistationary states (durations of the bright and dark periods), probabilities of quantum jumps, mean excitation levels of the quantized cavity mode, etc.     

The consensus times of the majority vote process on a torus

We study the majority vote process on a two-dimensional torus in which every voter adopts the minority of opinion with small probability . We identify the exponent that the mean of consensus time is asymptotically (1/) with that exponent as goes to 0. The proof is by a formula for mean exit time and by the metastable theory of Markov chains developed in the study of the stochastic Ising model.