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

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

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

The Steady-State Response of a Class of Dynamical Systems to Stochastic Excitation

In this paper a class of coupled nonlinear dynamical systems subjected to stochastic excitation is considered. It is shown how the exact steady-state probability density function for this class of systems can be constructed. The result is then applied to some classical oscillator problems

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

Building thermal load prediction through shallow machine learning and deep learning

Building thermal load prediction informs the optimization of cooling plant and thermal energy storage. Physics-based prediction models of building thermal load are constrained by the model and input complexity. In this study, we developed 12 data-driven models (7 shallow learning, 2 deep learning, and 3 heuristic methods) to predict building thermal load and compared shallow machine learning and deep learning. The 12 prediction models were compared with the measured cooling demand. It was found XGBoost (Extreme Gradient Boost) and LSTM (Long Short Term Memory) provided the most accurate load prediction in the shallow and deep learning category, and both outperformed the best baseline model, which uses the previous day's data for prediction. Then, we discussed how the prediction horizon and input uncertainty would influence the load prediction accuracy. Major conclusions are twofold: first, LSTM performs well in short-term prediction (1 h ahead) but not in long term prediction (24 h ahead), because the sequential information becomes less relevant and accordingly not so useful when the prediction horizon is long. Second, the presence of weather forecast uncertainty deteriorates XGBoost's accuracy and favors LSTM, because the sequential information makes the model more robust to input uncertainty. Training the model with the uncertain rather than accurate weather data could enhance the model's robustness. Our findings have two implications for practice. First, LSTM is recommended for short-term load prediction given that weather forecast uncertainty is unavoidable. Second, XGBoost is recommended for long term prediction, and the model should be trained with the presence of input uncertainty

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