Phase Transitions for the Brusselator Model

Dynamic phase transitions of the Brusselator model is carefully analyzed, leading to a rigorous characterization of the types and structure of the phase transitions of the model from basic homogeneous states. The study is based on the dynamic transition theory developed recently by the authors

Quark Mass Matrices from a Softly Broken U(1) Symmetry

Assigning U(1) charges to the quarks of the standard model, and allowing one extra scalar doublet with m^2 > 0, the correct pattern of the up and down quark mass matrices is obtained, together with their charged-current mixing matrix.Comment: 10 pages, no figur

Dynamic Model and Phase Transitions for Liquid Helium

This article presents a phenomenological dynamic phase transition theory -- modeling and analysis -- for superfluids. As we know, although the time-dependent Ginzburg-Landau model has been successfully used in superconductivity, and the classical Ginzburg-Landau free energy is still poorly applicable to liquid helium in a quantitative sense. The study in this article is based on 1) a new dynamic classification scheme of phase transitions, 2) new time-dependent Ginzburg-Landau models for general equilibrium transitions, and 3) the general dynamic transition theory. The results in this article predict the existence of a unstable region H, where both solid and liquid He II states appear randomly depending on fluctuations and the existence of a switch point M on the lambda-curve, where the transitions changes types

Subsidization Competition: Vitalizing the Neutral Internet

Unlike telephone operators, which pay termination fees to reach the users of another network, Internet Content Providers (CPs) do not pay the Internet Service Providers (ISPs) of users they reach. While the consequent cross subsidization to CPs has nurtured content innovations at the edge of the Internet, it reduces the investment incentives for the access ISPs to expand capacity. As potential charges for terminating CPs' traffic are criticized under the net neutrality debate, we propose to allow CPs to voluntarily subsidize the usagebased fees induced by their content traffic for end-users. We model the regulated subsidization competition among CPs under a neutral network and show how deregulation of subsidization could increase an access ISP's utilization and revenue, strengthening its investment incentives. Although the competition might harm certain CPs, we find that the main cause comes from high access prices rather than the existence of subsidization. Our results suggest that subsidization competition will increase the competitiveness and welfare of the Internet content market; however, regulators might need to regulate access prices if the access ISP market is not competitive enough. We envision that subsidization competition could become a viable model for the future Internet

Neutrino, Lepton, and Quark Masses in Supersymmetry

The recently proposed model of neutrino mass with no new physics beyond the TeV energy scale is shown to admit a natural and realistic supersymmetric realization, when combined with another recently proposed model of quark masses in the context of a softly broken U(1) symmetry. Four Higgs doublets are required, but two must have masses at the TeV scale. New characteristic experimental predictions of this synthesis are discussed.Comment: 7 pages, no figur

Quantum Monte Carlo Study of Pairing Symmetry and Correlation in Iron-based Superconductors

We perform a systematic quantum Monte Carlo study of the pairing correlation in the $S_4$ symmetric microscopic model for iron-based superconductors. It is found that the pairing with an extensive s-wave symmetry robustly dominates over other pairings at low temperature in reasonable parameter region. The pairing susceptibility, the effective pairing interaction and the $(\pi,0)$antiferromagnetic correlation strongly increase as the on-site Coulomb interaction increases, indicating the importance of the effect of electron-electron correlation. Our non-biased numerical results provide a unified understanding of superconducting mechanism in iron-pnictides and iron-chalcogenides and demonstrate that the superconductivity is driven by strong electron-electron correlation effects.Comment: Accepted for publication as a Letter in Physical Review Letters, and more discussions are adde

Degenerate Metric Phase Boundaries

The structure of boundaries between degenerate and nondegenerate solutions of Ashtekar's canonical reformulation of Einstein's equations is studied. Several examples are given of such "phase boundaries" in which the metric is degenerate on one side of a null hypersurface and non-degenerate on the other side. These include portions of flat space, Schwarzschild, and plane wave solutions joined to degenerate regions. In the last case, the wave collides with a planar phase boundary and continues on with the same curvature but degenerate triad, while the phase boundary continues in the opposite direction. We conjecture that degenerate phase boundaries are always null.Comment: 16 pages, 2 figures; erratum included in separate file: errors in section 4, degenerate phase boundary is null without imposing field equation

Stratified Rotating Boussinesq Equations in Geophysical Fluid Dynamics: Dynamic Bifurcation and Periodic Solutions

The main objective of this article is to study the dynamics of the stratified rotating Boussinesq equations, which are a basic model in geophysical fluid dynamics. First, for the case where the Prandtl number is greater than one, a complete stability and bifurcation analysis near the first critical Rayleigh number is carried out. Second, for the case where the Prandtl number is smaller than one, the onset of the Hopf bifurcation near the first critical Rayleigh number is established, leading to the existence of nontrivial periodic solutions. The analysis is based on a newly developed bifurcation and stability theory for nonlinear dynamical systems (both finite and infinite dimensional) by two of the authors [16]