Abstract:
We determine the ultimate fate of individual opinions in a socially-interacting population of leftists, centrists, and rightists. In an elemental interaction between agents, a centrist and a leftist can become both centrists or both become leftists with equal rates (and similarly for a centrist and a rightist). However leftists and rightists do not interact. This interaction step between pairs of agents is applied repeatedly until the system can no longer evolve. In the mean-field limit, we determine the exact probability that the system reaches consensus (either leftist, rightist, or centrist) or a frozen mixture of leftists and rightists as a function of the initial composition of the population. We also determine the mean time until the final state is reached. Some implications of our results for the ultimate fate in a limit of the Axelrod model are discussed.

Abstract:
We propose a general approach to study spin models with two symmetric absorbing states. Starting from the microscopic dynamics on a square lattice, we derive a Langevin equation for the time evolution of the magnetization field, that successfully explains coarsening properties of a wide range of nonlinear voter models and systems with intermediate states. We find that the macroscopic behavior only depends on the first derivatives of the spin-flip probabilities. Moreover, an analysis of the mean-field term reveals the three types of transitions commonly observed in these systems -generalized voter, Ising and directed percolation-. Monte Carlo simulations of the spin dynamics qualitatively agree with theoretical predictions.

Abstract:
We study the evolution of the Axelrod model for cultural diversity. We consider a simple version of the model in which each individual is characterized by two features, each of which can assume q possibilities. Within a mean-field description, we find a transition at a critical value q_c between an active state of diversity and a frozen state. For q just below q_c, the density of active links between interaction partners is non-monotonic in time and the asymptotic approach to the steady state is controlled by a time scale that diverges as (q-q_c)^{-1/2}.

Abstract:
We present a mathematical description of the voter model dynamics on heterogeneous networks. When the average degree of the graph is $\mu \leq 2$ the system reaches complete order exponentially fast. For $\mu >2$, a finite system falls, before it fully orders, in a quasistationary state in which the average density of active links (links between opposite-state nodes) in surviving runs is constant and equal to $\frac{(\mu-2)}{3(\mu-1)}$, while an infinite large system stays ad infinitum in a partially ordered stationary active state. The mean life time of the quasistationary state is proportional to the mean time to reach the fully ordered state $T$, which scales as $T \sim \frac{(\mu-1) \mu^2 N}{(\mu-2) \mu_2}$, where $N$ is the number of nodes of the network, and $\mu_2$ is the second moment of the degree distribution. We find good agreement between these analytical results and numerical simulations on random networks with various degree distributions.

Abstract:
A spinning nonextremal D3-brane undergoes a phase transition to a naked singularity which, from the braneworld point of view, corresponds to the apparent graviton speed passing from subluminal to superluminal. We investigate this phase transition from the dual perspectives of braneworld scenarios and holography. We discuss the relevance of the thermodynamic stability domains of a spinning D3-brane to the physics of braneworld scenarios. We also describe various gravitational Lorentz violations which arise from static D3-branes.

Abstract:
We calculate the absorption probabilities for a class of massless fields whose linear perturbations leave the near-extremal D3-brane background metric unperturbed. It has previously been found that, for extremal D3-branes, these fields share the same absorption probability as that of the dilaton-axion. We find that these absorption probabilities diverge from each other as we move away from extremality. The form of the corresponding effective Schrodinger potentials leads us to conjecture that the absorption of various fields by nonextremal D3-branes depends on the polarization of angular momentum.

Abstract:
We consider a brane world scenario which arises as the near-horizon region of a non-extremal D5-brane. There is a quasi-localized massive graviton mode, as well as harmonic modes of higher mass which are bound to the brane to a lesser degree. Lorentz invariance is slightly broken, which may have observable effects due to the leakage of the metastable graviton states into the bulk. Unlike a brane world arising from an extremal D5-brane, there is no mass gap. We also find that a brane world arising from a non-extremal M5/M5-brane intersection has the same graviton dynamics as that of a non-extremal D5-brane. This is evidence that a previously conjectured duality relation between the dual quantum field theories of each p-brane background may hold away from extremality.

Abstract:
We investigate the transition between singular and non-singular geometries from the vantage point of perturbative field dynamics. In particular, we obtain the closed-form absorption probability for minimally-coupled massless scalars propagating in the background of a heterotic 5-brane on a Taub-NUT instanton. This is an exact calculation for arbitrary incident frequencies. For the singular geometry, the absorption probability vanishes when the frequency is below a certain threshold, and for the non-singular case it vanishes for all frequencies. We discuss the connection between this phenomenon and the behavior of geodesics in this background. We also obtain exact quasinormal modes.

Abstract:
A new class of warped Anti-de Sitter solutions is found, arising as the near-horizon region of various semi-localized brane intersections. The dual gauge theories of AdS in warped spacetimes have reduced supersymmetry, which is pertinent to the study of viable supersymmetric extensions of the Standard Model. In addition, various supergravity solutions are probed via the absorption of various fields. In particular, we calculate exact absorption probabilities which provide finite-energy probes of supergravity solutions away from the conformal limit. Lastly, we discuss how brane world scenarios may arise from the near-horizon region of various p-brane configurations. Motivated by the dual non-commutative gauge theory, it is shown how a background B field mimics a negative four-dimensional cosmological constant, such that in both cases there is a massive four-dimensional graviton.

Abstract:
We consider five-dimensional domain-wall solutions which arise from a sphere reduction in M-theory or string theory and have the higher-dimensional interpretation as the near-horizon region of p-branes in constant, background B fields. We analyze the fluctuation spectrum of linearized gravity and find that there is a massive state which is localized and plays the role of the four-dimensional graviton.